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Let $0. Why $\sum r^{n!}$, $\sum r^{(2^n)}$ diverges as $r$ tends to $1$? It seems obvious since the limit of summand in $r$ is not zero, but the limit of summand in $n$ is zero.

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    What does "diverges as r tends to 1 mean "?2012-12-16
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    @Amr As r tends to 1, the sum tends to infinity.2012-12-16
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    If $N$ is fixed, what is $\lim\limits_{r\rightarrow1^-}\sum_{j=1}^N r^{j!}$?2012-12-16

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