An alternating series is a series where the terms are alternatively positive and negative.

- .
- .

- ;
- There exists a positive integer such that .

- For , the partial sum is an approximation of the sum of the series, with an error which is less than .
- The remainder and the first unused term have the same sign.

is an approximation of the sum of the series with an error less than .

In order to have an approximation of the sum of the series with an error less than , we must add the first 100 terms of the series (we get ).

Noah Dana-Picard 2007-12-28