For questions about recurrence relations, convergence tests, and identifying sequences.

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5
votes
2answers
200 views
+100

Finding a recurrence for a sum

I am trying to implement the following sum using a programming language: $$\sum_{i=1}^N a^i i^r$$ where $N$, $a$ and $r$ are integers. The problem is, I cannot find a suitable way to do this. ...
2
votes
1answer
184 views
+50

Partial sum of exponential series strictly increases after certain step

While trying to show that partial exponential series evaluated at two different values are strictly increasing provided that sufficient number of terms are applied I stuck at a problem. Given two ...