IA Type I -- Infinite Summation

[little penguin]

I'm at the second part, and I'm finding various values for T9 (a,x). To calculate this value, I type in each number in the sequence and then press enter (so I'd have to type 1 + 2ln2 + (2ln2)^2/2! + ... all the way up to (2ln2)^9/9!). This is incredibly time consuming. I was wondering if there is any more efficient way to find the T9 values? Maybe plugging in something into "Y=" and using something fancy to find the result?

Someone suggested taking a screenshot of my calculations and putting in the portfolio, but I can't imagine how that can be reasonable with the method I'm using now. It's just too long.

I have a TI-84 Plus, btw.

this is probably kinda late, but you can use Excel for that. it makes everything simple. if you need the Excel formulas, dig for the old posts, I swear I've posted it some time last January/February.

This confused me more haha. I have some time before my portfolio is due, so it would be great to hear back on how to do this!

[dessskris]

This confused me more haha. I have some time before my portfolio is due, so it would be great to hear back on how to do this!

here

why's it so difficult just to search on this thread???

the Excel formulas might be confusing esp if you are technologically challenged but please please put in the effort to TRY and follow the procedures I've written. it's your IA anyway. but if you are still lost come back here.

Edited July 30, 2011 by Desy Glau

[CkyBlue]

I'm at the second part, and I'm finding various values for T9 (a,x). To calculate this value, I type in each number in the sequence and then press enter (so I'd have to type 1 + 2ln2 + (2ln2)^2/2! + ... all the way up to (2ln2)^9/9!). This is incredibly time consuming. I was wondering if there is any more efficient way to find the T9 values? Maybe plugging in something into "Y=" and using something fancy to find the result?

Someone suggested taking a screenshot of my calculations and putting in the portfolio, but I can't imagine how that can be reasonable with the method I'm using now. It's just too long.

I have a TI-84 Plus, btw.

If you add me on Facebook one of my albums describes how to do it

[little penguin]

I figured it out! Thanks!

And sorry I couldn't find the post. I'm new to the website and still finding my way around. :/

As a follow-up question - should I put screenshots for every calculation or would it be sufficient to show one screenshot, show which functions I inputted, and say that I calculated everything using the same procedure?

The post with the Excel instructions also say, "When you want to tabulate other values of a and x, I suggest starting a new worksheet so you can use exactly the same formulas for Tn and Sn (look at the image posted below); because starting a new table will change the formulas a little bit and it is going to be very confusing unless you have learned how to use Ms. Excel before."

Does this mean simply changing the values of a and x in the current table will cause miscalculations in the Sn or Tn columns?

[dessskris]

I figured it out! Thanks!

And sorry I couldn't find the post. I'm new to the website and still finding my way around. :/

As a follow-up question - should I put screenshots for every calculation or would it be sufficient to show one screenshot, show which functions I inputted, and say that I calculated everything using the same procedure?

The post with the Excel instructions also say, "When you want to tabulate other values of a and x, I suggest starting a new worksheet so you can use exactly the same formulas for Tn and Sn (look at the image posted below); because starting a new table will change the formulas a little bit and it is going to be very confusing unless you have learned how to use Ms. Excel before."

Does this mean simply changing the values of a and x in the current table will cause miscalculations in the Sn or Tn columns?

lol alright it's okay.

if you use TI you'll have a history of calculations sort of thing so just put one screenshot showing all the calculation you did for every value of a and x. otherwise just use excel to generate tn and Sn, you don't need to use both calculator and Excel.

oh if you'd like to change the values of a and x only and then "save as" it would be fine too. just if you make a new table beside it then the formulas would have to change and it's difficult to teach excel over the internet so you better not trouble yourself lol (i'm so grateful I took a computer class where i learnt all this things in primary school!)

if you have further queries don't hesitate to ask.

[little penguin]

Thanks!

And for the screenshot: if I use excel only, would I have to show screenshots of every a and x value I will use in the portfolio or can I just show a screenshot of one calculation of a and x, briefly explain what I put into the spreadsheet, and say that I used the same procedure for all other values of a and x used?

[edit] ^This refers to the second part of the portfolio, where it asks you to find various values of Tn (a,x).

Finally - I completed the first part of the portfolio using a TI calculator. Would it be bad if I switched to using excel halfway through if I made it clear which method I used in which part?

Edited August 3, 2011 by little penguin

[gelleners]

How would I explain the part where it asks you to find a general statement that represents the infinite sum of this general sequence? I know the answer is supposed to be a^x which is the point on y that the asymptote approaches, but how would you explain how you found this?

[little penguin]

I have my values for T9 (2,x) plotted, and the exponential trendline fits perfectly, but the equation excel gives is based on an e value. Am I making a stupid mistake somewhere, or is there a setting on my ms excel that keeps setting the exponential equations to some power of e?

[dessskris]

Thanks!

And for the screenshot: if I use excel only, would I have to show screenshots of every a and x value I will use in the portfolio or can I just show a screenshot of one calculation of a and x, briefly explain what I put into the spreadsheet, and say that I used the same procedure for all other values of a and x used?

[edit] ^This refers to the second part of the portfolio, where it asks you to find various values of Tn (a,x).

Finally - I completed the first part of the portfolio using a TI calculator. Would it be bad if I switched to using excel halfway through if I made it clear which method I used in which part?

show all screenshots i.e. all tables you generated.

I suggest sticking to one method. Excel is easier. but if the first part in which you used TI was for the easier questions in the beginning I think it should be okay to use TI first and when you're asked to find more values use Excel.

---

How would I explain the part where it asks you to find a general statement that represents the infinite sum of this general sequence? I know the answer is supposed to be a^x which is the point on y that the asymptote approaches, but how would you explain how you found this?

with mathematical working? look into Taylor Expansion formula (if you use Ms.Word 2007 go to equation and select it from the built in equations menu)

need more help please ask.

---

I have my values for T9 (2,x) plotted, and the exponential trendline fits perfectly, but the equation excel gives is based on an e value. Am I making a stupid mistake somewhere, or is there a setting on my ms excel that keeps setting the exponential equations to some power of e?

hmmm I think in excel the exponential trendline is always e to the power of something and you can't change it. what are you looking for? you can opt to do the graph with TI.

[little penguin]

Thanks!

And for the screenshot: if I use excel only, would I have to show screenshots of every a and x value I will use in the portfolio or can I just show a screenshot of one calculation of a and x, briefly explain what I put into the spreadsheet, and say that I used the same procedure for all other values of a and x used?

[edit] ^This refers to the second part of the portfolio, where it asks you to find various values of Tn (a,x).

Finally - I completed the first part of the portfolio using a TI calculator. Would it be bad if I switched to using excel halfway through if I made it clear which method I used in which part?

show all screenshots i.e. all tables you generated.

I suggest sticking to one method. Excel is easier. but if the first part in which you used TI was for the easier questions in the beginning I think it should be okay to use TI first and when you're asked to find more values use Excel.

Hmm, ok. But since I'll be generating at least 25 different tables for 25 different values, would it be alright if I put these tables in an appendix?

I have my values for T9 (2,x) plotted, and the exponential trendline fits perfectly, but the equation excel gives is based on an e value. Am I making a stupid mistake somewhere, or is there a setting on my ms excel that keeps setting the exponential equations to some power of e?

hmmm I think in excel the exponential trendline is always e to the power of something and you can't change it. what are you looking for? you can opt to do the graph with TI.

The equation for the trendline I was looking at is actually y = 2^x. I was hoping excel would give me [number]^x, but it gave me e^[number]x instead.

I don't want to use the TI-84 for this, because I have no way of taking the screenshot and putting the graph into my portfolio. Could I instead explain the numbers that Sn approaches, and say that it fits the line y = 2^x?

[dessskris]

just put them in the main essay. examiners want to see them.

hmmm have you tried to use TI to plot the graph? it's worth trying. if it gives you your expected result then you should get a cable (borrow your friend's if you don't have one), connect it to your computer and install the TI software (I'm not sure where you can get this though. mine (TI-Nspire) was accompanied by the student software CD so I didn't need to get it from the net, it was very easy).

oh wait, I think you and I are confused with what a^x actually is. what is it? isn't it the S∞? so it's like the Sum you get when n becomes a very big number i.e. the maximum sum here. so it's not the equation of the graph.

I suggest just getting the best curve you can get in Excel and after you get the equation, for example it's y=508-5x^2 (which I don't think is correct but anyway...) since you're plotting Sn against n, your x is n and so when n=10 (do you find it till 10 or 9?) y=8 which is 2^3 and in this example a=2 and x=3 (x in the task, not x in the graph)

[mrmerlin]

Although your teacher is supposed to tell you this, however:

First you have to have a paragraph explaining what your project is about, what you're investigating and finally the method you're using. Also make sure you mention the 'technology' you're using, i.e GDC and whatever computer software you're going to use.

I read somewhere that we are supposed to write the IA without any "I" "we" etc, so Im not allowed to write sth like "I am using a TI-84+..." ? Shall I go to passive and say "A TI-84+ was used in this portfolio?" that sounds wierd imo

[dessskris]

I read somewhere that we are supposed to write the IA without any "I" "we" etc, so Im not allowed to write sth like "I am using a TI-84+..." ? Shall I go to passive and say "A TI-84+ was used in this portfolio?" that sounds wierd imo

actually I'm not so sure on that, but I've been told to avoid writing in first person in academic writings except in a TOK essay so if you can, please use passive voice. you can say "TI 84 was useful in the development of the task" or something.

[ChikkyD]

I read somewhere that we are supposed to write the IA without any "I" "we" etc, so Im not allowed to write sth like "I am using a TI-84+..." ? Shall I go to passive and say "A TI-84+ was used in this portfolio?" that sounds wierd imo

actually I'm not so sure on that, but I've been told to avoid writing in first person in academic writings except in a TOK essay so if you can, please use passive voice. you can say "TI 84 was useful in the development of the task" or something.

Definitely don't use I... it's a formal report, nobody is asking for a personal recount . And even the whole "was used" sounds odd. Go with what Desy said, and even expand on it by saying how it was used. But yeah, no "I"'s or "we"'s

[B2theRich]

I have read through this ENTIRE thread twice... and these are questions i have (answered or not already)

1.) Okay... This another task I have due in 6 days and I finished up to the part where i need to consider a general sequence where x =1 (3rd part on the first page).... and i'm lost and don't know where to begin with it

2.) Also, for the parts above it, where its just solving and graphing (which i am having trouble with). I used excel would i just copy the charts into my portfolio and have that be my calculations by explanation?

3.) (I know this was asked and answered a lot but I need my own clarification) The first page requires a general statement for all three parts and then one for the back (which I didn't start yet 0_0)

[dessskris]

1. similar to what you did for when a=2 and 3. try to do 3 more values, or as many as you need to see the pattern. then generalise it.

2. that's why i told you to connect your TI to your computer... you need to show the calculation (perhaps show the screenshot of your calculation from the GDC) of then plot the thing. you can use excel graph to plot but in TI it actually looks better IMO.

3. actually I think there is only one big general statement of S∞ (i.e. T∞(a, x)). the first page you need to find a narrower general statement for it in terms of a when x=1. the second page you need to find the big general statement.

[Razzker]

Hello there! I have the same task too.

1. similar to what you did for when a=2 and 3. try to do 3 more values, or as many as you need to see the pattern. then generalise it.

3. actually I think there is only one big general statement of S∞ (i.e. T∞(a, x)). the first page you need to find a narrower general statement for it in terms of a when x=1. the second page you need to find the big general statement.

1. So, since x=1 for all of the first part, I can generalize that as n approaches infinity, Sn will reach the value of a. Since x=1, is this correct?

3. I've noticed that a^x, but I'm not sure how to explain how I got that. I guess I can't simply say that I got it by trying out different values of a and x ... instead I researched online and got something like e^{(x ln a)} although I have no idea where the e came from ... any help?

[dessskris]

1. correct.

2. of course you can't... it's a maths paper so you need a mathematical explanation. tabulate all the values of a, x and T∞ and I'm sure you can then notice the pattern. you can find the general statement for each x first and then generalise again for all a and x.

e^(x ln a) is the same as a^x because the e and ln can cancel each other out it's from the taylor expansion. go to Ms Word, insert, equation (select from below), look at the third equation from the bottom. I hope you get how it relates to this task

Edited September 9, 2011 by Desy Glau

[Razzker]

Ah, yes! I think I've got it now. Thank you so much, Desy!

Okay, I've got another question. In the second part of the portfolio, it says "Define Tn(a,x) as the sum of the first n terms, for various values of a and x, e.g. T9(2,5) is the sum of the first nine terms when a = 2 and x = 5". What am I supposed to do here?

Edited September 9, 2011 by Razzker

[dessskris]

they're just telling you what T means. do you remember you're asked to define variables in the beginning of the type 2 IA? just do the same for this one basically they're just telling you a way to represent the sum thing.