Approximate the sum of the series correct to four decimal places.
sum from n=1 to infinity of ((-1)^(n+1))/(n^6)

Question

Approximate the sum of the series correct to four decimal places. 
sum from n=1 to infinity of ((-1)^(n+1))/(n^6)

anonymous · Answer

Would it help if I put it in equation form?

experimentx · Answer

no no that doesn't help ... use approximation for alternating series.

anonymous · Answer

how would I apply it?

experimentx · Answer

experimentx · Answer

find the term that starts from 5th decimal places ... and add up to that term only.

anonymous · Answer

okay so you would do the sum from n=1 to 5 of (-1)^(n+1)/(n^6)?

experimentx · Answer

anonymous · Answer

When you find the term that is less than $10^{-5}$ you know the 4th decimal place, and the places before it, will not be affected anymore.

experimentx · Answer

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