Newbetuts

Prove by Double Counting Method $\sum\limits_{k = 0}^m \binom{m}{k}\binom{n}{r + k} = \binom{m + n}{m + r}$ [duplicate]

Proof by induction of summation inequality: $1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\dots+\frac1{2^n}\ge 1+\frac{n}2$

How to prove $\sum^n_{i=1} \frac{1}{i(i+1)} = \frac{n}{n+1}$? [duplicate]

definite and indefinite sums and integrals

Evaluate $\sum_{n=1}^\infty 1/n^2$ using $\int_0^1 \int_0^1 \frac{\mathrm{d}x \, \mathrm{d}y}{1-xy}$

arccot limit: $\sum_{r=1}^{\infty}\cot ^{-1}(r^2+\frac{3}{4})$

Intuition behind sums of sums of whole numbers

How far can the convergence of Taylor series be extended?

How $\frac{1}{n}\sum_{i=1}^n X_i^2 - \bar X^2 = \frac{\sum_{i=1}^n (X_i - \bar X)^2}{n}$

Double induction example: $ 1 + q + q^2 + q^3 + \cdots + q^{n-1} + q^n = \frac {q^{n+1}-1}{q-1} $

Proving a summation inequality with induction

Is there a closed formula for this summation?

Show that $ \sum_{r=1}^{n-1}\binom{n-2}{r-1}r^{r-1}(n-r)^{n-r-2}= n^{n-2} $

A Vandermonde Identity for Stirling Numbers?

Closed form of Euler-type sum over zeta functions $\sum _{k=2}^{\infty } \frac{\zeta (k)}{k^2}$?

Expression for power of a natural number in terms of binomial coefficients

Proof by Induction: Solving $1+3+5+\cdots+(2n-1)$

New posts in summation

Prove by Double Counting Method $\sum\limits_{k = 0}^m \binom{m}{k}\binom{n}{r + k} = \binom{m + n}{m + r}$ [duplicate]

Testing convergence of series $\sum_{n=3}^\infty\frac{1}{n (\ln(n))^p(\ln\ln(n))^q}$

Mysterious subleading corrections to sums with internal dependence on limit

Show that the numerator of $1+\frac12 +\frac13 +\cdots +\frac1{96}$ is divisible by $97$

Proof by induction of summation inequality: $1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\dots+\frac1{2^n}\ge 1+\frac{n}2$

How to prove $\sum^n_{i=1} \frac{1}{i(i+1)} = \frac{n}{n+1}$? [duplicate]

definite and indefinite sums and integrals

Evaluate $\sum_{n=1}^\infty 1/n^2$ using $\int_0^1 \int_0^1 \frac{\mathrm{d}x \, \mathrm{d}y}{1-xy}$

arccot limit: $\sum_{r=1}^{\infty}\cot ^{-1}(r^2+\frac{3}{4})$

Intuition behind sums of sums of whole numbers

How far can the convergence of Taylor series be extended?

How $\frac{1}{n}\sum_{i=1}^n X_i^2 - \bar X^2 = \frac{\sum_{i=1}^n (X_i - \bar X)^2}{n}$

Double induction example: $ 1 + q + q^2 + q^3 + \cdots + q^{n-1} + q^n = \frac {q^{n+1}-1}{q-1} $

Proving a summation inequality with induction

Is there a closed formula for this summation?

Show that $ \sum_{r=1}^{n-1}\binom{n-2}{r-1}r^{r-1}(n-r)^{n-r-2}= n^{n-2} $

A Vandermonde Identity for Stirling Numbers?

Closed form of Euler-type sum over zeta functions $\sum _{k=2}^{\infty } \frac{\zeta (k)}{k^2}$?

Expression for power of a natural number in terms of binomial coefficients

Proof by Induction: Solving $1+3+5+\cdots+(2n-1)$