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Integral Test Problem?
Find the sum from n=2 to infinity of (e^(1/n))/(n^2).
I'm getting that it converges because the antiderivative is -e^(1/x) and that approaches 1 as x approaches infinity, meaning that both the improper integral and series converges; but the textbook says it diverges.
4 Answers
- Awms ALv 75 years agoFavorite Answer
It converges. You can also see it by
0 <= e^(1/n) / n^2 <= e / n^2
and the fact the sum of e/n^2 converges by the p-series test.
Unless there's a misunderstanding somewhere about what the problem is, I'd have to conclude the textbook is wrong in this case (mistakes happen)
- Anonymous5 years ago
74
- Anonymous5 years ago
there was clearly a mistake as sometimes that happens as you should email the textbook company as may even give you something in return
