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 | \![]() | \
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| 2 | \ ![]() | \
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| 3 | \ ![]() | \
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| 4 | \ ![]() | \
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| 5 | \ ![]() | \
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| 6 | \ ![]() | \
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| 7 | \ ![]() | \
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| 8 | \ ![]() | \
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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.