$\sum \frac{(n)^{1/2}}{(n+1)^3 * log(n)}$
I was hoping someone could tell me if this series converges and how to show that it does. Thanks in advance.
Convergence of series using which test?
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sequences-and-series
convergence
divergence
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0I apologize, the title is misleading. I just need to know if the series converges and using which methods. I edited the title – 2017-02-28
1 Answers
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Simple comparison:
$$\frac{n^{1/2}}{(n+1)^3\ln(n)}<\frac{n^{1/2}}{n^3}=\frac1{n^{2.5}}$$
And this clearly converges by the Cauchy condensation test, integral test, or p-series.