# Bound of error of alt. series

1. Apr 5, 2014

### syeh

1. The problem statement, all variables and given/known data
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

2. Relevant 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))

3. The attempt at a solution
|error|< U(sub10)
U(sub10) = 1/10^3
|error|< 1/1000

is this right..?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited: Apr 5, 2014
2. Apr 5, 2014

### Ray Vickson

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