Problem : Give an example of a series that converges but does not converge absolutely.
Consider the series
1 - + - + ^{ ... } |
Problem : Prove that (- 1)^{n} e ^{-n2 } converges.
The result follows from the alternating series test by noting that e ^{-(n+1)2 }≤e ^{-n2 } and that e ^{-n2 } = 0 .Problem : Determine whether or not
(- 1)^{n} |