New posts in summation

Let $a_k=\frac1{\binom{n}k}$, $b_k=2^{k-n}$. Compute $\sum_{k=1}^n\frac{a_k-b_k}k$

sequences-and-series elementary-number-theory summation binomial-coefficients contest-math

Rules of Double Sums

A sum with binomial coefficients

binomial-coefficients summation

A limit on binomial coefficients

limits binomial-coefficients summation

combinatorial proof of summation

combinatorics discrete-mathematics summation combinatorial-proofs

Closed form of $\sum\limits_{i=1}^n k^{1/i}$ or asymptotic equivalent when $n\to\infty$

sequences-and-series asymptotics summation closed-form

Is there any kind of formula to estimate this $1^1+2^2+3^3+...+n^n$? [closed]

summation infinity

Approximation of a summation by an integral

definite-integrals summation numerical-methods approximation summation-method

Inductive proof for $\binom{2n}{n}=\sum\limits_{k=0}^n\binom{n}{k}^2$

combinatorics summation induction binomial-coefficients

Induction problem: a formula for $\sum_{i=1}^n i(i+1)$

discrete-mathematics summation induction

Use Mathematical Induction to prove that $\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} +...+\frac{1}{n(n+1)}=1-\frac{1}{n+1}$ [duplicate]

discrete-mathematics summation induction

Help with telescoping sum $\sum_{i=3}^n \frac{1}{i(i+3)} $

real-analysis sequences-and-series summation telescopic-series

Evaluate $\sum_{n=1}^{\infty} \left( \arctan \frac{4n - 1}{2} - \arctan \frac{4n - 3}{2} \right)$

sequences-and-series summation

A nice combinatorial identity: $\sum_{k=1}^{n-1}\frac{\binom{k-1}{n-k-1}+\binom{k}{n-k-1}}{\binom nk}=1$

combinatorics summation binomial-coefficients

The sum of powers of $2$ between $2^0$ and $2^n$

algebra-precalculus summation geometric-progressions

Is this already an equation/law that has been found?

sequences-and-series summation

Evaluating $\sum_{n=1}^{\infty}\frac{(n-1)!}{\prod_{r=1}^{n}(x+r)}$ for $x\in\mathbb{R}^{+}$ [duplicate]

sequences-and-series summation

Simplify sum of factorials with mathematical induction

summation induction

Does parity matter for $\lim_{n\to \infty}\left(\ln 2 -\left(-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\cdots -\frac{(-1)^n}{n}\right)\right)^n =\sqrt{e}$?

real-analysis integration sequences-and-series limits summation

sum of product of three binomial coefficients

summation binomial-coefficients