1. ## Alternating Series

consider the series:
n=1 infinity
(-1)^n/( sqrt(n) +1) or

n=1 infinity
(-1)^n/(n!)^2

I understand that these series satisfy the alternating series test.

How many terms need to be added in order to reach within 10^-8 of the sum of the series?

I also need to figure out how to give a decimal approximation of the sum of one of these series with the maximum allowed error of 10^-8.

Thank you!

2. Originally Posted by brdun3
consider the series:
n=1 infinity
(-1)^n/( sqrt(n) +1) or

n=1 infinity
(-1)^n/(n!)^2

I understand that these series satisfy the alternating series test.

How many terms need to be added in order to reach within 10^-8 of the sum of the series?

I also need to figure out how to give a decimal approximation of the sum of one of these series with the maximum allowed error of 10^-8.

Thank you!
Let $S=\sum_{n=0}^{\infty}(-1)^na_n$ and $S_N=\sum_{n=0}^{N}(-1)^na_n$, then $R_N=\left|S-S_N\right|\leqslant{a_{N+1}}$. In other words the amount of error is less than or equal to the first neglected term.