An alternating series is a series where the terms are alternatively positive and negative.
(The alternating harmonic series)
Take a convergent alternating series
, as in Theorem 4.2.
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.
Take the alternating harmonic series
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