Bound of error of alt. series

  • Thread starter syeh
  • Start date
  • #1
15
0

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

 
Last edited:

Answers and Replies

  • #2
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,722
I think that 'third partial sum' means
[tex] \sum_{n=1}^3 (-1)^n \frac{1}{n^3} = -1 + \frac{1}{2^3} - \frac{1}{3^3}. [/tex]
 

Related Threads on Bound of error of alt. series

  • Last Post
Replies
1
Views
3K
Replies
0
Views
1K
Replies
1
Views
828
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
2
Views
833
Replies
7
Views
3K
  • Last Post
Replies
0
Views
4K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
7
Views
6K
Replies
1
Views
8K
Top