Question

It is important to distinguish between
\[
\sum_{n=1}^{\infty} n^{o} \quad \text { and } \quad \sum_{n=1}^{\infty} b^{n}
\]
What name is given to the first series? To the second? For what values of $b$ does the first series converge? For what values of $b$ does the second series converge?

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