The series $\backslash$sum$\_($n$=1)^(\backslash$infty $)((-1)^($n$+1))/(8$n$^(3))$ is a convergent alternating series $($this is easiest to verify with the Alternating

Series Test$).$ Suppose that this series converges to some value s$.$

Give an expression for the maximum error in an approximation of s by an m$^($th $)$ partial sum, s$\_($m$).$ Your

answer will involve the variable m :

Max. Error: $|$s$-$s$\_($m

Give the value of the index m which will guarantee an error less than or equal to $(1)/(10,000)$ by the

Alternating Series Remainder Theorem. This time, you should be able to get a value for m algebraically.

m$=$

Compute the m$^($th $)$ partial sum with your value of m found above. Round the answer to $5$ decimal places:

s$\_($m$)$~~