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Series: estimate sum within .01

  • Thread starter rcmango
  • Start date
  • #1
234
0

Homework Statement



How many terms of the series
infinity
E n =1

1/(1+n^2) must be added to estimate the sum within 0.01?

Homework Equations




The Attempt at a Solution



need help please. Also, the answer i believe it 100 terms. However i need to show work to support this answer.
 

Answers and Replies

  • #2
StatusX
Homework Helper
2,564
1
If we denote the infinite sum by S, ie:

[tex]S=\sum_{n=1}^\infty \frac{1}{n^2+1} [/tex]

and the partial sum of the first N terms by SN:

[tex]S_N=\sum_{n=1}^N \frac{1}{n^2+1} [/tex]

Then the error induced by estimating the infinite sum by the partial sum of the first N terms is:

[tex]S-S_N=\sum_{n=N+1}^\infty \frac{1}{n^2+1} [/tex]

Can you find an upper bound for this sum? Here's a hint: 1/(n-1)-1/n=1/n(n-1).
 
  • #3
234
0
while plugging numbers into n in the equation, i can see that the equation appears to approach to 0.

whats next :)
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,809
933
Yes, of course it approaches 0! "Next" is to answer your question: how large does n have to be to make it less than 0.01?
 

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