| The Alternating Series Test Suppose a series has the form
`a_1 - a_2 + a_3 - cdots +text[(]-1text[)]^ka_k + cdots`,
where
- each `a_k` is positive,
- each `a_k` is larger than `a_(k+1)` , and
- `lim_(k rarr oo) a_k=0`.
Then
- the series converges to some number `S`, and
- the error `text[|] S-s_n text[|]` after summing `n` terms is less than `a_(n+1)`.
|