# Math Help - Series

1. ## Series

Hello all,.. need help with this one :
Given the series

$S = 1 - \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} - \frac{1}{\sqrt{4}} + \cdots$

If $S_n$ denote the partial sum of the first n term of this series, determine n such that the difference between $S$ and $S_n$ is less than 0.001.

any idea?
thx a lot.

2. Originally Posted by dedust
Hello all,.. need help with this one :
Given the series

$S = 1 - \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} - \frac{1}{\sqrt{4}} + \cdots$

If $S_n$ denote the partial sum of the first n term of this series, determine n such that the difference between $S$ and $S_n$ is less than 0.001.

any idea?
thx a lot.
For an alternating series the error can not be larger then the next term in the series.