Series..

ZHero · 2008-07-17 06:47:12

How do I sum the following series to 'infinity'...?

mathsyperson · 2008-07-17 07:30:49

So you want to know the value of

.
Dividing this by 7 gives , which is a bit nicer, and you can multiply by 7 again at the end.

I did this by writing this in terms of summations that don't involve squares on the top, then wrote that in terms of summations with only constants on the top, and then that can be evaluated directly because it's a bunch of geometric series. There might be a better way that I've missed, but this way works at least.

I'll only do the first bit, because it's quite long.

(ie. the first k terms of the sequence)

Then divide by 6 to get S. So we have:

You can use a similar method to find

in terms of sums with only numbers on the numerators, and so with lots of plugging stuff in you can arrive at a final answer (by replacing k with infinity at the end).

Hopefully you followed that. Whether you did or not, the sum in your question comes to 49/18.
I confirmed this by adding the first 10 or so terms on a calculator and watching them converge to it.

ZHero · 2008-07-17 07:47:09

Thanks mathsyperson!
I did follow the steps but was wondering why this question has been put on the '30 second questions' sections in the book that i'm reading for an 'entrance exam preparation'!?
Great Job all the way.. Thanks again!

Daniel123 · 2008-07-17 08:03:47

ZHero wrote:

Thanks mathsyperson!
I did follow the steps but was wondering why this question has been put on the '30 second questions' sections in the book that i'm reading for an 'entrance exam preparation'!?
Great Job all the way.. Thanks again!

Is it an entrance exam for the 'school of ridiculously quick mental mathematics'?

mathsyperson · 2008-07-17 08:39:59

Yeah, I have no idea how you could possibly find the exact answer in that amount of time.
It could be possible if the question was multiple choice though.

Say you got given something like:

a) 0
b) 7/6
c) 49/18
d) π
e) ∞

Then you could maybe get it in that time, on the assumption that one of the answers is right.
If it's a straight question with no information other than what you've said, then there must be some really nice and simple method that we're not seeing.

ZHero · 2008-07-17 23:41:43

You're right mathsyperson!
Its a multiple choice question with 5 options (fractions) and the solution is given as 'Don't try to solve it! Find the approx decimal values of choices and choose the one with the nearest approx decimal value of the given series...' which again, i believe, is not an easy job!!

Math Is Fun Forum

#1 2008-07-17 06:47:12

Series..

#2 2008-07-17 07:30:49

Re: Series..

#3 2008-07-17 07:47:09

Re: Series..

#4 2008-07-17 08:03:47

Re: Series..

#5 2008-07-17 08:39:59

Re: Series..

#6 2008-07-17 23:41:43

Re: Series..

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