Let f (x) = (x -arctanx) /(x ^3 )for each x ≠ 0 Find the power series with sum equal to f (x) (when | x | ≤ 1, x ≠ 0), and use this power series to calculate the limit limx → 0f (x).

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- July 27th 2014, 07:04 PMHaytham1111A Series question
Let f (x) = (x -arctanx) /(x ^3 )for each x ≠ 0 Find the power series with sum equal to f (x) (when | x | ≤ 1, x ≠ 0), and use this power series to calculate the limit limx → 0f (x).

- July 27th 2014, 08:31 PMSlipEternalRe: A Series question
What have you tried? Do you know the power series for ? Have you tried just plugging that in and simplifying?

- July 27th 2014, 08:55 PMHaytham1111Re: A Series question
Yes i did, i got series (-1)^(n+1) *x^(2n-2) (series from n=1 to infinity)

But it was not the correct answer

The correctly answer is ∑k=0∞((−1)^k)/(2k+3)*x^(2k)

1/3

I do not understand how he get this answer. Have you any suggestion? - July 27th 2014, 09:25 PMSlipEternalRe: A Series question

The first term of the series is x. So, when you perform the subtraction, you get:

Then, dividing by gives the series

- July 28th 2014, 03:47 AMHaytham1111Re: A Series question
Thank you. It is the same i got, but i should reindeks the series to start from n=0 .

I am leserinnlegg Latex and i use texmaker. How i can write the dokument in latex in this forum. Can you help? - July 28th 2014, 05:47 AMSlipEternalRe: A Series question