(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the sum of the series [tex]\sum[/tex][tex]^{\infty}_{0}[/tex][tex]\frac{(-9)^{n}}{(2n+1)!}[/tex]

2. Relevant equations

Alternating series Estimation Theroem

3. The attempt at a solution

I think it satisfies the conditions necessary for an alternating series to converge. The limit as n approaches infinity of b[tex]_{n}[/tex]=0, and b[tex]_{n}[/tex]>b[tex]_{n+1}[/tex]. So listing out the terms I get 1-(9/6)+(81/120)-(720/5040)+... But at this point I'm not sure how far to expand the series, because the problem just says find the sum of the series, which makes me think that there would be an exact answer, but I can't think of another way to find a sum. It's not a geometric sequence, and I don't think I could estimate it with integration either.

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# Homework Help: Sum of the Series

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