The sequence is .
The term representation of the sequence is
.
The partial sum of the sequence for terms is
.
Now tabulate the partial sum for different values of .
n | \an | \sn | \
1 | \![]() | \
![]() | \
2 | \ ![]() | \
![]() | \
3 | \ ![]() | \
![]() | \
4 | \ ![]() | \
![]() | \
5 | \ ![]() | \
![]() | \
6 | \ ![]() | \
![]() | \
7 | \ ![]() | \
![]() | \
8 | \ ![]() | \
![]() | \
The sum of first eight terms of the sequence is .
Observe the partial sum of sequence, .
The partial sum appears to be increasing.
\So the sequence is divergent.
\The sequence is divergent.