(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the sum to three decimal places

[itex]\sum^{\infty}_{n=1}[/itex][itex]\frac{1}{n^{3}}[/itex]

2. Relevant equations

3. The attempt at a solution

So the following is the method that I learned how to do it.. but I think it is wrong.

[itex]\int^{\infty}_{n}[/itex][itex]\frac{dx}{x^{3}}[/itex]

to get

[itex]\frac{1}{2n^{2}}[/itex]

I then take that and do

[itex]\frac{1}{2n^{2}}[/itex][itex]\leq[/itex]0.0005

solving for n gets n=31.6

so there should be 32 terms for the sum to be accurate to 3 decimal places.

But I think I'm wrong because when I plug 32 in for n of the original function, I get something like 0.0000305. But how would anything like that small affect the third decimal place?

Thanks!

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# Trying to find the number of terms in a series so it is accurate to 3 decimal places

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