IA Type I -- Infinite Summation

[itsme]

i was wondering for part 2 of the ia (when given T for sum instead of S) it says plot the relation between T and x. does this mean at the end after testing different x values while a=2 you plot those different x values you chose with their respective sum?

[Nasraq]

For part one of the question, I'm curious... Are we suppose to simply plug in numbers?

Also, I'm kinda confused as to terms.

When it says "calculate the sums Sn of the first n terms from 0 to 10" does it mean T0 = 1? And so on? So it'd be 1+ ....

Is T0 the first term? or T1 the first term?

I have a feeling that there will be 2 general statements for part 2. One for >3 and one for

hmmmmmm

Edited December 13, 2010 by Nasraq

[Angiemac]

Can somebody please help me! I don't know how to do any part of the portfolio. I don't even know how to write one and the whole sequence and series thing is my worst subject in math so I have no idea what I'm doing and the portfolio is due in 5 days. Can somebody give me any hints or advice?

[computerlove]

Doesn't the log property of pulling down the exponent only work if it's ln(2^2) and not (ln2)^2?

I'm getting a^x too but without pulling it down...

[Jarrell Lewis]

How do you find the sum of the sequence using Excel?

[Antrikshy]

This is a great thread, going on for months. But I'm disappointed that there is no answer here yet.

I am really confused. I need to submit my portfolio the day after tomorrow, and I really do not understand the Part D, with the "general sequence". Can someone explain it real quick?

[commie]

OK guys! this math IA is considered to be hard one...

I ll give you this link http://www.slideshare.net/ellenmckay/ib-sl-math-ia-1-2

there is some guy doing this ia, he will not get all points, because the way he got formula is more like guessing, than normal mathematical approach. But it is helpful for people who suck with explanations and reflections! And he did all the counting job for us...

To get the formula i would recommend to look at Maclaurin series and Taylor series, from them you can arrive to the true formula a^x! (basically just substitute some part of your formula into the series, and from the log rules get the general statement)

[1212matt1212]

OK guys! this math IA is considered to be hard one...

I ll give you this link http://www.slideshare.net/ellenmckay/ib-sl-math-ia-1-2

there is some guy doing this ia, he will not get all points, because the way he got formula is more like guessing, than normal mathematical approach. But it is helpful for people who suck with explanations and reflections! And he did all the counting job for us...

To get the formula i would recommend to look at Maclaurin series and Taylor series, from them you can arrive to the true formula a^x! (basically just substitute some part of your formula into the series, and from the log rules get the general statement)

The first obvious mistake this person made was rounding to six decimals. In the directions it clearly says that all answers should be correct to six decimals. This is because the point of this is to realize that there will be a limit. This portfolio makes me feel good about mine, but I feel bad for Ellen McKay, who won't be getting her Diploma, since she posted her portfolio online..

[commie]

I guess she has bunch of mistakes, i looked again at it, and i take my words back. The calculations in her IA are wrong, she even faked the data at some point. Ln(1) equals to 0, not 1 as she wrote, to try to fit the pattern. And she clearly does not understand the concept of asymptote... Use that IA to understand how IA should not look like.

And to get most of the points do not forget to say the values of x and a for which the formula will not work. This is really important - examiners will take bunch of points from ur math criteria.

[Cynthia]

I have a feeling that there will be 2 general statements for part 2. One for >3 and one for

hmmmmmm

Just one general statement.

[Nasraq]

Well I think it's important to note that the asymptote doesn't apply to all the parts of the question. When asked to graph the first 11 terms, it is understandable to have an asymptote, but when asked for the general statement, it says as n approaches infinity, what does Sn become. In this case, it will eventually add up to a or a^x, asymptote or not.

[Mahuta ♥]

This is a great thread, going on for months. But I'm disappointed that there is no answer here yet

The whole point of this thread is to help you to find the right answer, not the give you them.

Try sharing the ideas you're getting with the others and you might reach the answer with their ideas.

[Noxen]

Hey everybody. I have seen this question arise in a couple cases of this discussion... all very general though. My main question is the initial summing process. For one, I am confused as whether to use t₀ or t₁ as the first term in the sequence. My guess is that because the assignment says to find the sum of 0<=n<=10, that you do use t₀ as your first term. Also, when finding S_n of the first 11 terms (at least I think it is the first 11), should I add each term manually, or use the equation S_n=(a (1-r ⁿ))/(1-r). Finally, when it says express your answers... does that mean I should keep a "running total" of S_n for each term... and then graph each total against n on the graph(s) which I need to do.

I will probably have more questions later... however I just need a little help getting started. I have experimented with a few different methods of summing, but I just find myself going back and having to change something or getting unrealistic answers. Any help would be appreciated .

Thanks

[dessskris]

Hey everybody. I have seen this question arise in a couple cases of this discussion... all very general though. My main question is the initial summing process. For one, I am confused as whether to use t₀ or t₁ as the first term in the sequence. My guess is that because the assignment says to find the sum of 0<=n<=10, that you do use t₀ as your first term. Also, when finding S_n of the first 11 terms (at least I think it is the first 11), should I add each term manually, or use the equation S_n=(a (1-r ⁿ))/(1-r). Finally, when it says express your answers... does that mean I should keep a "running total" of S_n for each term... and then graph each total against n on the graph(s) which I need to do.

I will probably have more questions later... however I just need a little help getting started. I have experimented with a few different methods of summing, but I just find myself going back and having to change something or getting unrealistic answers. Any help would be appreciated .

Thanks

Hello I hope it's not too late for me to reply now. I am not doing this portfolio task and I am not going to do it, but since it's holiday and I am sick of my HW, I am just interested in helping people with their math portfolios

I apologise if my thoughts do not make sense or whatever.. It might be because I'm not doing this task and not putting a lot of effort in doing it

I am confused as whether to use t₀ or t₁ as the first term in the sequence.

t₀ should be the first term in the sequence. Your guess is correct IMO. They say 0<=n<=10 and they give its value anyway (t₀ = 1). So yes.

when finding S_n of the first 11 terms (at least I think it is the first 11), should I add each term manually, or use the equation S_n=(a (1-r ⁿ))/(1-r)

Yup first 11 terms, and I am not so sure but I think you should add each term manually. That Sn formula is of a geometric sequence, right? FYI this sequence is not a geometric sequence, if you thought it was. Why? Because in a geometric sequence, the ratio must always be the same, right? But in this case it's not. So you actually can't use that Sn formula. Let me know if it doesn't make sense to you and I would make this clearer. So add them up manually. And it says 'calculate' anyway..

From Mathematics HL Guide 2008, page 71

Calculate: Obtain the answer(s) showing all relevant working.

when it says express your answers... does that mean I should keep a "running total" of S_n for each term... and then graph each total against n on the graph(s) which I need to do

Express your answers? Where? I don't see any part in this task saying express so idk what you are talking about but I guess that's "Give your answers correct to six decimal places."?

This question asks you to to find S0, S1, S2, S3, ... , S9 and S10.

And then yes you plot a graph of Sn against n.

Good luck! I hope my answers make sense. and I don't mind helping again if you have further questions

[Noxen]

Thanks for your response! It really helps... and no your not too late . As promised... I have another question . I am at the point where you need to make your first "general statement." Over the course of my calculations and summing, I found that the final sum of a sequence is approximately equal to its a value if rounded to the nearest whole number. This in mind, should I just say that the sum equals the a value? I am confused how I should structure/find my general statement. Also, I think this applies to the second "general sequence" in the assignment. Is that the place where people are talking about the statement being a^x?

Thank you so much for your help so far!

[Summer Glau]

As x approaches infinity, Sn approaches/equals ______ . That's how I structured my GS. As for whether x approaches or equals the a value, I suggest you try using a few more decimal places than recommended just to see what happens to Sn. (you don't necessarily have to write this on your portfolio) From this I think you'll find the answer to your question

[ruahmhisen94]

i am stuck on this infinite summation internal assessment. please help

the question is asking

using technology plot the relation between S_n and n. describe what you notice from your plot. what does this suggest about the value of S_n as n approaches ∞ ?

please help quick thanks

[dessskris]

You are welcome

I am at the point where you need to make your first "general statement." Over the course of my calculations and summing, I found that the final sum of a sequence is approximately equal to its a value if rounded to the nearest whole number. This in mind, should I just say that the sum equals the a value? I am confused how I should structure/find my general statement.

I've just calculated the sums when x=1 and a=2 too..and yes apparently it approaches 2. I suggest you using your GDC and showing a screenshot of the calculations then, if possible

Hmm you do realise that it is a Mathematics portfolio, right?

Criterion A: use of notation and terminology

Achievement level 2: The student uses appropriate notation and terminology in a consistent manner and does so throughout the work.

(Mathematics HL Syllabus 2008; page 73)

I think it should be the same for SL.

So I would suggest writing:

S_∞ = a

Or something like that. I guess what fire.realm suggested should be fine, though. But my Math teacher doesn't like words and she wants us to use mathematical notations so if I were you I'd write that ^

I think this applies to the second "general sequence" in the assignment. Is that the place where people are talking about the statement being a^x?

Yes I think so.

---

i am stuck on this infinite summation internal assessment. please help

the question is asking

using technology plot the relation between S_n and n. describe what you notice from your plot. what does this suggest about the value of S_n as n approaches ∞ ?

please help quick thanks

Er... So?

What do you need help with? Specify your question.

using technology plot the relation between S_n and n.

Use a graphing software to graph S_n against n. I personally recommend Autograph.

describe what you notice from your plot

I don't really know (I'm not doing this portfolio ) but maybe you should describe the shape of the curve..? Hint: it kind of plateaus off at the end

what does this suggest about the value of S_n as n approaches ∞ ?

S_∞ = something

[InSaNeMaGiC]

I am really confused on how to use the Taylor series to arrive at the equation.......

[dessskris]

I am really confused on how to use the Taylor series to arrive at the equation.......

Do you have to use Taylor series? :/

I am not doing this portfolio but I thought I could just help.

I do not really know about Taylor series, either.. Seriously. Just googled it but I don't quite understand

BUT I think you can arrive at the equation even without using the Taylor series (because I did find the equation without it).

Which part are you at? Have you calculated the sum Sn for the first n terms of the first sequence for 0<=n<=10? Have you plotted the relation between Sn and n?

If you have, I'd suggest looking at the graph til you see that it plateaus off, approaching a certain value which is actually something related to the sequence. Then it IS your equation. So you can actually do it without knowing the Taylor series -- unless your teacher told you to use Taylor series :/

I hope I'm driving you to the right direction perhaps..