# Math Help - Alternating Series Sums

1. ## Alternating Series Sums

How many terms (at least) of the alternating series E from n=1 to infinity (-1)^(n+1) 1/(n^2) must we add to be sure that the partial sum S(N) approximates the sum S of the series with error less than 0.0001?

(a) 10
(b) 50
(c) 100
(d) 120
(e) 150

2. Originally Posted by leilani13
How many terms (at least) of the alternating series E from n=1 to infinity (-1)^(n+1) 1/(n^2) must we add to be sure that the partial sum S(N) approximates the sum S of the series with error less than 0.0001?

(a) 10
(b) 50
(c) 100
(d) 120
(e) 150
alternating series w/ decreasing terms to 0 ... error < |first omitted term|

error $< \frac{1}{n^2} < \frac{1}{10000}$

so ... what $n$ will work?

3. 100?

4. Originally Posted by leilani13
100?
you don't sound so sure ...

5. I didn't understand where
Originally Posted by skeeter
error $< \frac{1}{n^2} < \frac{1}{10000}$
came from. But, I understand now.