4
$\begingroup$

I have the following series: $\sum_{n=1}^{\infty} \frac{n}{\sqrt{n(n + 1)(n + 2)}}$

I must investigate if it is divergent or convergent. I have tried different approaches like the root test, but it didn't help me:(. Could someone point me in the right direction?

Best regards, Petar

1 Answers 1

10

For large $n$, the $n$th term of your series is roughly $\frac{1}{\sqrt{n}}$. Can you think of another series whose convergence/divergence behavior is known and whose terms can be compared with $\frac{1}{\sqrt{n}}$? Try using the comparison test between your original series and the new series.

  • 0
    Than$k$s for the suggestion! This is what I was missing.2011-02-06