How Accurate Is the Ninth Partial Sum of an Alternating Series?

[syeh]

Homework Statement

if the series ∑(n=1, goes to infinity) (-1)^n/(n^3)
is approximated by its ninth partial sum, find a bound for truncation error

Homework Equations

Alternating Series Estimation Thm:
If alternating series is CONVERGENT, then truncation error for nth partial sum is less than U(sub(n+1)) and has the same sum as the first unused term:

|error|< U(sub(n+1))

The Attempt at a Solution

|error|< U(sub10)
U(sub10) = 1/10^3
|error|< 1/1000

is this right..?

Homework Statement

Homework Equations

The Attempt at a Solution

 

[Ray Vickson]

I think that 'third partial sum' means
$$\sum_{n=1}^3 (-1)^n \frac{1}{n^3} = -1 + \frac{1}{2^3} - \frac{1}{3^3}.$$