How many terms of :(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n^2} [/tex]

do you have to add to get an error < .01

Alright, I used the Alternating Series Estimation Theorem since the terms are decreasing and the terms approach 0.

So, by the theorem, .01 < = [tex] b_{n+1} [/tex] so

[tex] 1/(n+1)^2 = 1/100[/tex]

[tex] (n+1)^2 = 100 [/tex]

[tex] n+1 = 10[/tex]

So this means that in order to get this error, we have to add 9 terms right? The back of my book says 10 is the answer. Why is that?

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# Estimating a sum of an Infinite series

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