IA Type I -- Infinite Summation

[dessskris]

Hi,

I also feel the same way as Nasraq. As I am calculating a=3 and x=7, my results seem to be approaching 2184, not 2187. Am I doing something wrong, because 3^7 certainly is 2187 so why aren't my results approaching that number? I'm Frustrated

Thanks in advance.

Is that the question on the second page, let a=3 and calculate T₉(3, x) for various positive values of x? Well the question only asks you the sum of the first nine terms.. Only 9 terms! And as the value of x increases, the value of T₉ will be farther away from the value that you expect it to approach. You will then need to find T₁₀, T₁₁, T₁₂, T₁₃ and so on and so forth to see that it approaches a^x.

For a=3 and x=7, right, try calculating until T₂₅. I just got 2187. (thanks to TI-Nspire Student Software).

EDIT: heeey you deleted your post already!! haha wtv..

[Jas]

Hey, I have the same assignment as you.

The general formula is a^x. Your value for a should be the point on the y axis at which the asymptote approaches. Good luck

How can it be a^x? shouldn't it be ax?

ummm I’m not sure how you can get a general formal unless I’m completely off track... I thought the asymptote was y=0 but now I’m just confused.

[dessskris]

Hey, I have the same assignment as you.

The general formula is a^x. Your value for a should be the point on the y axis at which the asymptote approaches. Good luck

How can it be a^x? shouldn't it be ax?

ummm I’m not sure how you can get a general formal unless I’m completely off track... I thought the asymptote was y=0 but now I’m just confused.

Well, I don't think y=0 is an asymptote (y=0 is the x-axis), but are you sure you meant y=0? Maybe x=0 (the y-axis) yeah it might be considered an asymptote, but I don't really think so. But then you have a horizontal asymptote which actually is y=a^x as IBSlayer said.

[Jas]

Hi guys i just got this assignment 2 days ago and im very confused.

for the question where it says

"Now consider a general sequence where x=1. Calculate the sum Sn of the first n terms of this gernal sequence for between 0 and 10 fir diferent values of a"

Do i use the formula that looks like this : Sn =

a - ar^n

----------

1 - r

If so, how do i find r?

...it's not a geometris sequence...you don't use that formula

i think you need to find your own formula

Hey, I have the same assignment as you.

The general formula is a^x. Your value for a should be the point on the y axis at which the asymptote approaches. Good luck

How can it be a^x? shouldn't it be ax?

ummm I’m not sure how you can get a general formal unless I’m completely off track... I thought the asymptote was y=0 but now I’m just confused.

Well, I don't think y=0 is an asymptote (y=0 is the x-axis), but are you sure you meant y=0? Maybe x=0 (the y-axis) yeah it might be considered an asymptote, but I don't really think so. But then you have a horizontal asymptote which actually is y=a^x as IBSlayer said.

oh you're right! i just fixed my brackets on excel....and one of my graphs went under the x axis... fail. but thanks no i just need to make sense of all my clutered graphs and equations...

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

you need to find "LN" in the functions... and "!" <-- factorial is also a funtion... but it's "FACT" in excel's funtion list.

They've given us a new math internal assessment about infinite summation. But I couldn't find anything on the internet and I really need help because I did not understand anything!!!!!! its deadline is 4 days from now! If there's anyone who already solve it please help me!

Post by: Mahuta

2 TOPICS MERGED

I'm having some trouble with the second part of this. What does it mean when it says T9 (2,5) is the sum of the first nine terms when a=2 and x=5 ??

T9 mean you need to find the first nine terms using a = 2 and x = 5

then {T9(2,5)} = the sum of the first nine terms....get it? [T9 (2,5)] is just like a variable kinda... like X

[AznKid]

Hi,

I have this portfolio too, and can someone tell me if the general statement for the first part and the second part of the portfolio the same?

Or are they different? I'm kind of confused with this statement.

Also, i have found out that the general statement will not work when a < 0., that is the limitation. Is there any other limitations i'm missing?

Thanks

[dessskris]

Hi,

I have this portfolio too, and can someone tell me if the general statement for the first part and the second part of the portfolio the same?

Or are they different? I'm kind of confused with this statement.

Also, i have found out that the general statement will not work when a < 0., that is the limitation. Is there any other limitations i'm missing?

Thanks

I'm confused which is the first part and which is the second part? I assume the second part is the one on the second page yeah..

The general statement must be the same. In the first part, x=1 so a^x=a¹=a

For the limitation,

I don't really know since I'm not doing the portfolio, so I am not putting in a lot of effort in finding the answer but I roughly can guess the answer..

I would suggest testing when values of a and x are:

- positive integer

- negative integer

- positive fraction

- negative fraction

- zero

- surd (e.g. √k)

- log k

- ln k

- e^k

- kπ

(k is a constant)

And try to mix them like maybe when a=log 5 and x=-√2 or something like that..

[Summer Glau]

Hi,

I have this portfolio too, and can someone tell me if the general statement for the first part and the second part of the portfolio the same?

Or are they different? I'm kind of confused with this statement.

Also, i have found out that the general statement will not work when a < 0., that is the limitation. Is there any other limitations i'm missing?

Thanks

I'm confused which is the first part and which is the second part? I assume the second part is the one on the second page yeah..

The general statement must be the same. In the first part, x=1 so a^x=a¹=a

For the limitation,

I don't really know since I'm not doing the portfolio, so I am not putting in a lot of effort in finding the answer but I roughly can guess the answer..

I would suggest testing when values of a and x are:

- positive integer

- negative integer

- positive fraction

- negative fraction

- zero

- surd (e.g. √k)

- log k

- ln k

- e^k

- kπ

(k is a constant)

And try to mix them like maybe when a=log 5 and x=-√2 or something like that..

No, the general statements are not the same. It tells you to find a general statement for part one, then tells you to find a general statement for part two. Sorry but you're supposed to find the limitations of the general statement yourself Like Desy mentioned, try using different types of numbers as a and x values. You can find the limitation(s) this way.

EDIT: Sorry I just realized that the first part isn't a general statement, only the second one is Either way, the pattern you find for the first part and the pattern for the second part are not the same.

Edited January 2, 2011 by Summer Glau

[mousetrap]

I am confused about scope. is there anyone who can explain me what do i supposed to explain for scope?

[Jas]

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?

That was my understanding....but people are telling me a gillion different ways for the back so i'm really confused, i'm pretty sure it's like you said....but i don't even know.

[InSaNeMaGiC]

How do you find the equation mathematically? It says explain how you arrived at the equation mathematically....

[jenmhn]

okay, after carefully reading many of these posts, i want to clarify.

in total, there should only be ONE general statement?

that would mean the sentence at the bottom (use your observations . . . find a general statement) goes along with the back of the page?

[dessskris]

Uhh sorry I am not really helpful in here..instead I am confusing people! Sorry sorry!

How do you find the equation mathematically? It says explain how you arrived at the equation mathematically....

Do it by algebra..?

okay, after carefully reading many of these posts, i want to clarify.

in total, there should only be ONE general statement?

that would mean the sentence at the bottom (use your observations . . . find a general statement) goes along with the back of the page?

As Summer Glau said, yeah one general statement

Sorry I was confused because I think some people referred to S_∞ on the first page as a general statement so I thought there were 2 general statements hahaha

There is only one GS then, which is the one you just mentioned

[InSaNeMaGiC]

That really didn't help.....

I want to know if there is any sort of method to go from the sequence to a^x, I mean I can see it through patterns that arise

But I think there is supposed to be a mathematical approach, can anyone explain it to me.....

[Galaxy_11]

I'm on the first page and i see the relation between a and S_n but I'm not so sure about the general statement. Could I get a hint? Also, do you need a general formula to get the general statement?

[hithere0.0]

Hi, this is from an IB kid anyhow it is 2 In the morning, Im doing an IA report, and I wanted to know How in the work Sn approaches 2, and not 0.

2 hours and this is due................... :[

anyone clarify if its one general statement, or two seperate ones?

Edited January 5, 2011 by Mahuta ♥

[dessskris]

Hi, this is from an IB kid in philly PAAAAAAAAAAAAAAAAAAAAA, anyhow it is 2 In the morning, Im doing an IA report, and I wanted to know How in the work Sn approaches 2, and not 0.

fml, 2 hours and this is due................... :[

anyone clarify if its one general statement, or two seperate ones?

first off, dont spam! haha

I am not doing this task but perhaps I could still help?

firstly you need to find Sn when n approaches infinity right? on the first page. dont call that a general statement, but yeah you need to find it

and then on the second page they ask you the real general statement, the T9 thingy..

[InSaNeMaGiC]

Hey everyone, do this assignment on your own, this thread will just confuse you, it did not help me at all. Also you will get more out of it by doing it by yourself. Just go and do it by yourself and it will be much better. It will take less time to find out what to do on your own than looking through this thread, because it is just very confusing, no offence to the guys who tried to help.

Also take a look at the Taylor Series for finding the equation a^x mathematically

Edited January 5, 2011 by InSaNeMaGiC

[carrot]

How on EARTH can you do the 1st question : calculate the sum Sn of the first n terms of the above sequence for o<n<10 (o and 10 included)???

Anyone done this 'Infinite summation' math portfolio type 1 already? please help!

Am also doing this coursework.

I've done the two specific ones where x=1, a=2 and where x=1, a=3 but am now trying to do the general sequence for a where x=1 and am not sure how to go about this. I've written this out in full 10∑r=0(ln a )^n/n! but have no idea where to go from there. If anyone could give me some indication of how i'm meant to start adding these would be a massive help!

Thanks.

so how do you do the first specific ones where x=1 and a=2?

how do i do this?

[dessskris]

How on EARTH can you do the 1st question : calculate the sum Sn of the first n terms of the above sequence for o<n<10 (o and 10 included)???

Anyone done this 'Infinite summation' math portfolio type 1 already? please help!

Am also doing this coursework.

I've done the two specific ones where x=1, a=2 and where x=1, a=3 but am now trying to do the general sequence for a where x=1 and am not sure how to go about this. I've written this out in full 10∑r=0(ln a )^n/n! but have no idea where to go from there. If anyone could give me some indication of how i'm meant to start adding these would be a massive help!

Thanks.

so how do you do the first specific ones where x=1 and a=2?

how do i do this?

If 0<n<10, 0 and 10 are not included

But if 0<=n<=10, 0 and 10 are included

How on earth can't you use your calculator to calculate Sn when 0<=n<=10 and the sums???

Then at the end you can use Taylor Series to find the general statement as InSaNeMaGiC said.

[mackdaddy]

Hi, I am working on my IA and am having trouble graphing the sequences.

For example, tn=(ln2)^n)/n!)

I believe the reason I am having trouble graphing is because of the undefined solutions in between the terms.

Any help would be appreciated.

Thanks

Also, I would like to graph the summation of the terms... any idea as to how to correctly put it in the calculator?