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3
questions
4
votes
0
answers
162
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Determine sum of the series $\sum_{k=1}^\infty\frac{1}{n(n+1)(n+2)}$ [duplicate]
I have the following problem,
$$\sum_{k=1}^\infty\frac{1}{n(n+1)(n+2)}$$
And I try to work as follows:
Hint: Partial Fraction decomposition:
$\begin{aligned}
\frac{1}{n(n+1)(n+2)} &= \frac{...
- 3,919
1
vote
3
answers
116
views
Find the limit of the sequence $\left( \sqrt {2n^{2}+n}-\sqrt {2n^{2}+2n}\right) _{n\in N}$
My answer is as follows, but I'm not sure with this:
$\lim _{n\rightarrow \infty }\dfrac {\sqrt {2n^{2}+n}}{\sqrt {2n^{2}+2n}}=\lim _{n\rightarrow \infty }\left( \dfrac {2n^{2}+n}{2n^{2}+2n}\right) ^{\...
- 39
8
votes
2
answers
1k
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Infinite Product $\prod_{n=1}^\infty\left(1+\frac1{\pi^2n^2}\right)$
How do I find:
$$\prod_{n=1}^\infty\; \left(1+ \frac{1}{\pi ^2n^2}\right) \quad$$
I am pretty sure that the infinite product converges, but if it doesn't please let me know if I have made an error.
...
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