Newbetuts

Dealing with a difficult sum of binomial coefficients, $\sum_{l=0}^{n}\binom{n}{l}^{2}\sum_{j=0}^{2l-n}\binom{l}{j} $

Combinatorial interpretation of a sum identity: $\sum_{k=1}^n(k-1)(n-k)=\binom{n}{3}$

Summation by parts of $\sum_{k=0}^{n}k^{2}2^{k}$

Proving an identity involving factorials

How should I solve combination addition like this?

Proving $\sum_{k=0}^n\binom{2n}{2k} = 2^{2n-1}$ [duplicate]

Closed form of integral over fractional part $\int_0^1 \left\{\frac{1}{2}\left(x+\frac{1}{x}\right)\right\}\,dx$

Show that the sum of reciprocal products equals $n$

Is it possible to express $\frac{1}{n}+\frac{1}{1+n}+\dots+\frac{1}{2n-1}$ as a sum

Combinatorial reasoning for the identity $\left ( \sum_{i=1}^n i \right )^2 = \left ( \sum_{i=1}^n i^3 \right ) $ [duplicate]

Given a finite set U, how can we enumerate all subsets of U that have an odd number of elements [duplicate]

How to simplify this summation containing floor

New Year Maths 2015

Sums of $5$th and $7$th powers of natural numbers: $\sum\limits_{i=1}^n i^5+i^7=2\left( \sum\limits_{i=1}^ni\right)^4$?

The value of $\sum_{1\leq l< m <n}^{} \frac{1}{5^l3^m2^n}$ [closed]

Hint proving this $\sum_{k=0}^{n}\binom{2n}{k}k=n2^{2n-1}$

New posts in summation

Why are these two functions so close in value? [closed]

On the sum of digits of $n^k$

Exercise involving DFT

Handling different summation limits

Dealing with a difficult sum of binomial coefficients, $\sum_{l=0}^{n}\binom{n}{l}^{2}\sum_{j=0}^{2l-n}\binom{l}{j} $

Combinatorial interpretation of a sum identity: $\sum_{k=1}^n(k-1)(n-k)=\binom{n}{3}$

Summation by parts of $\sum_{k=0}^{n}k^{2}2^{k}$

Proving an identity involving factorials

How should I solve combination addition like this?

Proving $\sum_{k=0}^n\binom{2n}{2k} = 2^{2n-1}$ [duplicate]

Closed form of integral over fractional part $\int_0^1 \left\{\frac{1}{2}\left(x+\frac{1}{x}\right)\right\}\,dx$

Show that the sum of reciprocal products equals $n$

Is it possible to express $\frac{1}{n}+\frac{1}{1+n}+\dots+\frac{1}{2n-1}$ as a sum

Combinatorial reasoning for the identity $\left ( \sum_{i=1}^n i \right )^2 = \left ( \sum_{i=1}^n i^3 \right ) $ [duplicate]

Given a finite set U, how can we enumerate all subsets of U that have an odd number of elements [duplicate]

How to simplify this summation containing floor

New Year Maths 2015

Sums of $5$th and $7$th powers of natural numbers: $\sum\limits_{i=1}^n i^5+i^7=2\left( \sum\limits_{i=1}^ni\right)^4$?

The value of $\sum_{1\leq l< m <n}^{} \frac{1}{5^l3^m2^n}$ [closed]

Hint proving this $\sum_{k=0}^{n}\binom{2n}{k}k=n2^{2n-1}$