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Type I -- Infinite Summation

ballon

By ballon
in Maths SL

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aronnax

aronnax

Posted
Posted (edited)

Okay, I think I may have the answer but am terribly confused with the Taylor Series. I may also have got one of the log formulas so I am hoping this is the answer. If I'm revealing things I should not be revealing, please feel free to stop me.

So... is this how you work out the general statement from the Taylor series?

<Use Log rules to play around until you get the answer>

Compare graphs from T9 (a, x) with a^x to confirm them.

Conclusion. Is that right?

Please let it be right...

Edited by aronnax
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Guest 1529

Guest 1529

Posted
Posted (edited)

Okay, I think I may have the answer but am terribly confused with the Taylor Series. I may also have got one of the log formulas so I am hoping this is the answer. If I'm revealing things I should not be revealing, please feel free to stop me.

So... is this how you work out the general statement from the Taylor series?

[Deleted Working]

Compare graphs from T9 (a, x) with a^x to confirm them.

Conclusion. Is that right?

Please let it be right...

First of all, yeah, you shouldn't be posting it like this... you cannot reveal equations and expression that YOU have deduced so what I suggest is that you edit your post and erase that working bit. But I can tell you that the working it's right ;)

The general statement is what you actually observe from the plots and the values of the sequences that you have done comparing with the "theory" (a^x), I believe...

And the T9 is actually to show you how the change in x affects the plot. That's all I can say :S

Edited by 1529
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Asukers

Asukers

Posted
Posted

Hi guys,

this is also my first IA and I'm somewhat getting it...?!

Anywho, can someone tell me about the format of an IA? I have most of my calculations done, I just don't know how to put it together.

What sorts of things do we mention in the intro?

To what extent do we have to show our working?

Does the general statement suffice as a conclusion?

Thanks in advance!

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dessskris

dessskris

Posted
Posted

Hi guys,

this is also my first IA and I'm somewhat getting it...?!

Anywho, can someone tell me about the format of an IA? I have most of my calculations done, I just don't know how to put it together.

What sorts of things do we mention in the intro?

To what extent do we have to show our working?

Does the general statement suffice as a conclusion?

Thanks in advance!

General (recommended) format of a Math IA

Outline for this IA task

Show all working and calculations.

Your conclusion includes the general statement but you need to mention some other things too.

If still in doubt just ask!

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dessskris

dessskris

Posted
Posted

Okay, you're welcome :)

I don't know either, sorry, but I think they are pretty much the same thing. It's basicly asking you to state the conditions in which the general statement is true, usually the domain of the variables. Like can a and x be negative, rational numbers, zeroes or real numbers? Stuffs like that.

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Dredgon1

Dredgon1

Posted
Posted

My teacher,apparently...Hmm...I haven't tamed my TI-89 that much yet, so, when I get to that stage I will come back to you to seek assistance on how to properly operate it if possible...

Thanks for your help.

By the way, is the sequence that is being used an Infinite Geometric Sequence? I just wanted to be sure...

Oh haha ok. Btw I thought it was the stellar numbers IA haha that's why I was like how the heck could you use excel for this?? lol I think Ms. Excel works best for this infinite summation IA.

How to Use Ms. Excel 2007 for Infinite Summation IA

  • Open your Ms. Excel 2007
  • In cell B2, put a
  • In cell C2, put x
  • In cell D2, put n
  • In cell E2, put Tn
  • In cell F2, put Sn
  • Merge cells B3 to B13 (Select these cells, On the Home tab, in the Alignment group, click Merge and Center)
  • Put the desired value of a in cell B3
  • Merge cells C3 to C13
  • Put the desired value of x in cell C3
  • Put 0 to 10 in cells D3 to D13 (values of n)
  • Type in the formula =(($C$3*LN($B$3))^D3)/FACT(D3) in cell E3
  • Copy that cell and paste in cells E4 to E13
    infinitesummationexcel.jpg
  • Type in the formula =SUM($E$3:E3) in cell F3
  • Copy that cell and paste in cells F4 to F13
    infinitesummationexcel2.jpg
  • Select cells E3 to F13
  • Right click, Format Cells, Number, Category: Number, Decimal Places: 6, OK
  • 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.
    infinitesummationexcel3.jpg
  • You may want to take a screenshot and put it in Ms. Word so you do not need to calculate one by one the values of Tn and Sn. Do not forget to mention that you use Ms. Excel here.

And NO, it is NOT an Infinite Geometric Sequence. It is an infinite sequence, but it's not geometric.

You wouldn't by any chance know how to do that on a mac? I have Excel:mac 2008 and it seems different.

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mikadpn

mikadpn

Posted
Posted

Hey everyone, I'm new to IBSurvival but it seems like its extremely helpful!

I got this IA not long ago and I have it due this monday and this is what I have so far...

I found Sn for the terms of 0 < n < 10 for both x=1 , a=2 and x=1 , a=3 and what I saw is that as n approaches infinity, Sn approaches the value of (a), although it never truly gets it (unless you round) so I figured that (a) must be an asymptote of some kind... The problem then came when I said to choose my own values of (a) while x=1 and my guesses about (a) were fine when i tried a=4 a=6 and a=10 but when I chose numbers such as a=1/2 and a=1/4, it made no sense because some of my values for Sn were greater than (a)

To calculate everything I am using my calculator by doing: sum(seq((1*Ln(a)^x)/x! , x , 0 , n) and I plug in values for a and n to find the value of Sn.

The main problem so far is the a=1/2 which basically proved me wrong and threw me off track :S .

Also, I saw that people were saying that the general term was a^x but the only reason I agree is because I tried it out, for example, if X=1 and A=10, and I do Sn=A^x, (Sn being 10) then 10=10^1 , and It seems to work fine.

How do you guys think I'm doing? This is my second IA so far, I did one about population trends in China last time and that resulted in an all-nighter.. :S

I really appreciate all the help that I can get!

Thank you very much!

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dessskris

dessskris

Posted
Posted

first off, welcome to IBS! :welcome: I hope you'll find this forum useful and contribute back too. :)

your IA is due monday and you've only finished the first part? :blink: good luck then.

are you sure it does? hmm TBH I haven't tried with fractions (non-integers) but if your calculation is correct then you can mention it as your scope/limitation.

S∞=ax when a∈Z or something along those lines. do you think a can be negative btw? if not then it would be a∈Z+.

I think you should quickly finish it so that you won't need to pull another all nighter for this IA. wish you the best luck! :gluck:

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mikadpn

mikadpn

Posted
Posted

first off, welcome to IBS! :welcome: I hope you'll find this forum useful and contribute back too. :)

your IA is due monday and you've only finished the first part? :blink: good luck then.

are you sure it does? hmm TBH I haven't tried with fractions (non-integers) but if your calculation is correct then you can mention it as your scope/limitation.

S∞=ax when a∈Z or something along those lines. do you think a can be negative btw? if not then it would be a∈Z+.

I think you should quickly finish it so that you won't need to pull another all nighter for this IA. wish you the best luck! :gluck:

Thanks! You're reply was really helpful! I've done a lot of progress so far! :D No all-nighter for me today!

Also, thank you so much for the explanation on using excel for this IA, it REALLY speeds up the process, before I was only using my GDC and it would take forever!

If you need help with anything, I'll try my best to provide it ;)

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dessskris

dessskris

Posted
Posted

My math class has the same portfolio too :) It must be a generic IB assigned project.

Mathematics IA tasks are actually produced by the IB... they produced a number of tasks from which the teacher can choose one type 1 task and one type 2 task to give to their students :) so it's not surprising to see a lot of people from other parts of the world doing the same IA task as you :P

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ips2012

ips2012

Posted
Posted

I don't get it for the second page, the one where they ask you to find the Tn=(a,x).

THey ask you for the sum of the first 9th terms, but this is going to be a very large value that is going to increase exponentialy, right? Help. Its due soon,

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