Alternating Series Partial Sum

  • Thread starter Nick_L
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  • #1
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Can anyone help me out with calculating the partial sum of an alternating series? For example, how would I find the sum correct to 4 decimal places of:

CalcProblem.gif


What I tried was finding how many terms it would take the have an error that was < .0001 then found the sum with that many terms... I got 0.10969 as the partial sum using 4 terms.
 

Answers and Replies

  • #2
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Note that

[tex]\sum_{n=1}^{\infty}nx^n=\frac{x}{(x-1)^2}[/tex]

which can be obtained from the geometric series by computing the derivative and multiplying by x. Hence

[tex]\sum_{n=1}^{\infty}n(-\frac{1}{11})^n=-\frac{11}{144}[/tex]
 

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