Problem :
Give an example of a series that converges but does not converge absolutely.
Consider the series
Convergence follows from the alternating series test, whereas absolute convergence
fails because the harmonic series diverges.
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} 

converges.
The series converges by the alternating series test, since the absolute value of
the
nth term in the series is
Notice that the convergence is not absolute.