How Many Terms of the Alternating Series $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n + 1 } n ^ { - 2 }$

Multiple Choice

How many terms of the alternating series $\sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n + 1 } n ^ { - 2 }$ must we add in order to be sure that the partial sum $S _ { n }$ is within 0.0001 of the sum $S$ ?

A) 10
B) 300
C) 30,000
D) 30
E) 3
F) 10,000
G) 100
H) 1000