Homework Help: Series approximation

1. Apr 4, 2009

remaan

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

Using the sum of the first 10 terms ,
Estimate the sum of the series (1/n^2) n from 1 to infinity ? How good the estimate is ?

c) Find a value for n that will ensure that the error in the approximation s= sn is less than .001.

2. Relevant equations

I think Rn = s - sn

3. The attempt at a solution

Am ok with that, but how to know who good the appr. is ??
And do we do the integration to find the value of n ? if so please tell how ?

Last edited: Apr 4, 2009
2. Apr 4, 2009

Tom Mattson

Staff Emeritus
Check your book for a remainder theorem associated with the integral test. Is it there?

3. Apr 4, 2009

remaan

Uha, I think that you mean this formula

Sn+ ∫_(n+1 )^(infity )▒〖f(x)dx<s<Sn+ ∫_n^(infinity )▒f(x)dx〗

Do you think that this works for part c ?

4. Apr 4, 2009

Tom Mattson

Staff Emeritus
Your equation doesn't appear as it should on my browser, but there's a simple theorem for estimating the remainder $R_N$ that exists when the nth partial sum $S_N$ of a convergent series is computed. It says:

$$R_N\leq a_N+\int_N^{\infty}f(x)dx$$

And yes, it will help for part c.

5. Apr 4, 2009

remaan

Uha, thanks alot..

But, I still wondering when do we use two boundries and when to use only one when computing the error ??

6. Apr 4, 2009

Tom Mattson

Staff Emeritus
You're not computing the error, you're estimating it. And any series that converges by the integral test has only positive terms. So there is always an implicit lower boundary of 0 on $R_N$.