- #1

- 1,235

- 1

[tex] \sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n^{2}} [/tex], [tex] | error | < 0.01 [/tex]. So, [tex] b_{n} = \frac{1}{n^{2}} [/tex]. [tex] b_{n} < b_{n+1} [/tex], and [tex] \lim_{n\rightarrow \infty} b_{n} = 0 [/tex]. Therefore, the series is convergent. I wrote out some terms of the series: [tex] s = 1-\frac{1}{4}+\frac{1}{9}-\frac{1}{16}+\frac{1}{25}-\frac{1}{36}+\frac{1}{49}-\frac{1}{64}+\frac{1}{81}-\frac{1}{100}+\frac{1}{121}+ . . . [/tex]. From this step, how do we determine the number of terms we need to add in order to find the sum to the indicated accuracy?

Thanks