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Results tagged with sequences-and-series
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user 51505
for questions about sequences and series, e.g. convergence, closed form expressions, etc. Note that there is a different tag for spectral sequences, and also note that MathOverflow is not for homework. Please consider consulting the online encyclopedia for integer sequences, if you are trying to identify a given sequence that you have found in your research.
7
votes
Accepted
Is there a simple proof of the following Identity for $\sum_{k=m-1}^l(-1)^{k+m}\frac{k+2}{k+...
We obtain for $l,m\in\mathbb{N}$ with $0\leq m-1 \leq l$:
\begin{align*}
\color{blue}{\sum_{k=m-1}^{l}}&\color{blue}{(-1)^{k+m}\frac{k+2}{k+1}\binom{l}{k}\binom{k+1}{m}}\\
&=\frac{1}{m}\sum_{k=m- …
- 516
3
votes
Accepted
Is there a simple proof of the following binomial Identity (part 2)?
Following the hint @darijgrinberg stated in the comment section with respect to the beauty inside the square brackets we focus on the sum and
we obtain
\begin{align*}
\color{blue}{\sum_{k=m+ …
- 516