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Type I -- Infinite Summation


ballon

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Sorry for asking so many questions. I have found that the general statement is ax, but I don't see any limitations to this general statement. Any help? Hints maybe?

Also, I know that the Taylor expansion works for this paper, but I cannot explain how I know this. I don't think the teacher will believe me if I just say that I found the equation on MS Word and that it matches. Haha.

Edited by Razzker
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it's okay, it's not very many ;) I've got A LOT more questions than that. a few more won't hurt.

the limitation, what if a and x becomes zero? what if they become negative? what if they become fractions? what if they become surds? etc... stuff like that.

lol, I don't know... I mean, I was also only told by someone a long long time ago. maybe say that you are reminded of this formula... and if your teacher asks, just say you found it from the internet when researching on this task.

I think someone said it's in their textbook or something like that. can you try looking it up in your book? maybe you can find it there :S

EDIT: it's in the HL syllabus! just say some HL student told you about it or something? :S

Edited by Desy Glau
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Let's just say I researched online. Hehe ...

Anyway, I'm almost done with the portfolio. Thank you so much for your help. I finally found a way to explain how I got the general statement and all I need to do now is to complete the document with headers and footers, a cover page and other fancy stuff.

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Hey so I was wondering what the implications are for the series if a is negative, or even an imaginary number, a square root of a negative number. Does anyone have any ideas on these as excel just came up with errors for ives and imaginery values of a?

Edited by hugo262
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for the first section where x=1, the general statement is that n=sn where n is the limit for sn.

however on the second part of it when you change the x value, the general statement is a^x :)

i found at first that my statement was ax but double and triple check your equation (i used excel) because if you don't write it right then this is the pattern you'll get!! hope this saves time as it wasted a lot of mine!!!

Good luck IBlets :D

Edited by laneey
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Okay, thanks! I ended up using Geogebra to graph because I already did my calculations on the GDC and maunally copied to Word in MathType, so I didn't want to retype everything in Excel.

I'm at the last part of the portfolio now; does anyone mind explaining the difference between the validity and scope/limitations of the general statement? Are they both just values of a and x that would result in the statement being false? IF so should I group them into one category?

Also, is continue with this analysis to find the gernal statement... the same thing as explain how you arrived at the general statement? IB.. so many command terms and questions.. :P

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oh you can do it in Ms.Word too. can't believe you didn't know that! D: use the chart feature thing. but oh well.

validity: they're asking for some kind of 'informal' proof. if you could give a formal, mathematical prove (which is not expected at SL level, only at HL) that would be super awesome. otherwise you could try for some other values of a and x, investigate and check with your general statement.

scope/limitations: what can a and x be? can they be zero? can they be negative? can they be decimals? can they be pi or e? etc... and is there any other limitation? well you'll have to figure that out. yes this part is asking for values of a and x where the general statement will be false.

no don't group them into one category.

and sorry i don't quite understand your last question? when they ask you to explain how you arrived at the general statement, well they wonder how you got the formula -_-

I personally think this could be explained when you are about to generate the general statement, but that's just me. ask your teacher for some certainty.

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  • 2 weeks later...

Hey guys, i just got my internal assessment today.

I really did not understand anything that the assignment says. However after reading this post I have noticed that there are some ideas of the general statement being a^x or ax

What is this whole idea behind Taylor's Expansion, i looked it up online and it seems to be the answer to the whole calculations to ultimately find the general statement.

Is there anyone out there that could help me and give me a direction that I could follow

thank you soo much.

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to both of you, and all the other people who need help, the outline for this IA can be found here:

Taylor expansion can be used to prove or validate the general statement.

if you still don't get the answer to your question from the very detailed outline, ask again. but please quote me so I get a notification so I can reply to you as soon as I check this website.

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Hey so I am at the part where you have to calculate the sum of the first ten terms when x=1 and a is not defined. How can I add the different values to a sum if T1= (ln a)/1! and T2= (ln a)/2! and so forth?

lol you're so cute! you should set the values of a by yourself, I suggest trying for at least 3-5 different values of a. then you should see a pattern and generalise for any value of a :)

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