Step 1:
\The series .
Consider and
.
Find the ten partial sums of the series by considering a table.
\![]() | \
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1 | \0.4472 | \0.4472 | \
2 | \0.7071 | \1.1543 | \
3 | \0.8320 | \1.9863 | \
4 | \0.8944 | \2.8807 | \
5 | \0.9284 | \3.8091 | \
6 | \0.9486 | \4.7577 | \
7 | \0.9615 | \5.7192 | \
8 | \0.9701 | \6.6893 | \
9 | \0.9761 | \7.6654 | \
10 | \0.9805 | \8.6459 | \
\
Step 2:
\Divergence test:For the series , If
, then the series
is divergent.
Find
If
Since , then the series
is divergent.
Solution:
\The series is divergent.
\