Newbetuts

Prove that ${\sum\limits_{n=1}^{\infty}}(-1)^{n-1} \frac{H_n}{n} = \frac{\pi^2}{12} - \frac12\ln^2 2$

How find this sum $ \frac{1}{1999}\binom{1999}{0}-\frac{1}{1998}\binom{1998}{1}+\cdots-\frac{1}{1000}\binom{1000}{999}$

What is the sum over a shifted sinc function?

Combinatorial proof that binomial coefficients are given by alternating sums of squares?

Asymptotic expansion of $\sum _{k=1}^n \left(\frac{k}{n}\right)^k$

proof of $\sum\nolimits_{i = 1}^{n } {\prod\nolimits_{\substack{j = 1\\j \ne i}}^{n } {\frac{{x_i }}{{x_i - x_j }}} } = 1$ [duplicate]

Minimal value of $\sum_{1\leq i<j\leq 2014}a_ia_j$ where $a_i=\pm1$

Find the limit of $\sum\limits_{k=1}^n\left(\sqrt{1+\frac{k}{n^2}}-1\right)$

Euler-Maclaurin summation for $e^{-x^2}$

Applications of Switching Sums and Integrals

Formula for $1^k+2^k+3^k...n^k$ for $n,k \in \mathbb{N}$

Using right-hand Riemann sum to evaluate the limit of $ \frac{n}{n^2+1}+ \cdots+\frac{n}{n^2+n^2}$

Alternative combinatorial proof for $\sum\limits_{r=0}^n\binom{n}{r}\binom{m+r}{n}=\sum\limits_{r=0}^n\binom{n}{r}\binom{m}{r}2^r$

Intuitive ways to get formula of cubic sum

How to show $\frac{19}{7}<e$

Combinatorics Identity about Catalan numbers: $\sum_{k=0}^n \frac{1}{k+1}\binom{2k}k \binom{2n-2k}{n-k}=\binom{2n+1}n$

Asymptotic analysis of $\sum_{k=2}^n\frac{k}{\ln k}$

Proving $\sum_{k=0}^{n}k{n\choose k}^2 = n{2n-1 \choose n-1} $

New posts in summation

Prove that ${\sum\limits_{n=1}^{\infty}}(-1)^{n-1} \frac{H_n}{n} = \frac{\pi^2}{12} - \frac12\ln^2 2$

Where do summation formulas come from?

Summation of series $\sum_{k=0}^\infty 2^k/\binom{2k+1}{k}$

How find this sum $ \frac{1}{1999}\binom{1999}{0}-\frac{1}{1998}\binom{1998}{1}+\cdots-\frac{1}{1000}\binom{1000}{999}$

What is the sum over a shifted sinc function?

Combinatorial proof that binomial coefficients are given by alternating sums of squares?

Asymptotic expansion of $\sum _{k=1}^n \left(\frac{k}{n}\right)^k$

proof of $\sum\nolimits_{i = 1}^{n } {\prod\nolimits_{\substack{j = 1\\j \ne i}}^{n } {\frac{{x_i }}{{x_i - x_j }}} } = 1$ [duplicate]

Minimal value of $\sum_{1\leq i<j\leq 2014}a_ia_j$ where $a_i=\pm1$

Find the limit of $\sum\limits_{k=1}^n\left(\sqrt{1+\frac{k}{n^2}}-1\right)$

Euler-Maclaurin summation for $e^{-x^2}$

Applications of Switching Sums and Integrals

Formula for $1^k+2^k+3^k...n^k$ for $n,k \in \mathbb{N}$

Using right-hand Riemann sum to evaluate the limit of $ \frac{n}{n^2+1}+ \cdots+\frac{n}{n^2+n^2}$

Alternative combinatorial proof for $\sum\limits_{r=0}^n\binom{n}{r}\binom{m+r}{n}=\sum\limits_{r=0}^n\binom{n}{r}\binom{m}{r}2^r$

Intuitive ways to get formula of cubic sum

How to show $\frac{19}{7}<e$

Combinatorics Identity about Catalan numbers: $\sum_{k=0}^n \frac{1}{k+1}\binom{2k}k \binom{2n-2k}{n-k}=\binom{2n+1}n$

Asymptotic analysis of $\sum_{k=2}^n\frac{k}{\ln k}$

Proving $\sum_{k=0}^{n}k{n\choose k}^2 = n{2n-1 \choose n-1} $