New posts in summation

Evaluating the limit : $\displaystyle \lim_{n \to \infty} \dfrac{1}{\sqrt{n}} \displaystyle \sum_{k=1}^n \dfrac{1}{\sqrt{n+k}}$

summation riemann-sum

A question from the dreams realm

functions convergence-divergence summation

Does $\sum_{k=0}^{\infty}\sin\left(\frac{\pi x}{2^k}\right)$ have a simple form with interesting properties?

sequences-and-series summation trigonometric-series

Identity involving double sum with factorials

summation binomial-coefficients factorial pochhammer-symbol

A proof of the identity $ \sum_{k = 0}^{n} \frac{(-1)^{k} \binom{n}{k}}{x + k} = \frac{n!}{(x + 0) (x + 1) \cdots (x + n)} $.

combinatorics summation binomial-coefficients

If integration is a continuous analog of summation (Addition), what is the continuous analog of multiplication (Product)?

integration summation products

Sum with binomial coefficients: $\sum_{m=1}^{k}\frac{1}{m^{2a}}\binom{k}{m}$ with constant a

combinatorics summation binomial-coefficients binomial-theorem

How to calculate summation of $\frac{n^2 + n + 1 }{n^2 + n}$ over $1$ to $25$?

discrete-mathematics summation

Help me prove this inequality :

sequences-and-series inequality summation

How find this interesting sum $\sum_{n=1}^\infty\ln(f(n))+\ln(g(n))$

summation

Sum of $1+\frac{1}{2}+\frac{1\cdot2}{2\cdot5}+\frac{1\cdot 2\cdot 3}{2\cdot 5\cdot 8}+\cdots$

sequences-and-series summation

Why is this sum equal to $0$?

sequences-and-series analysis summation products

Contest math problem: $\sum_{n=1}^\infty \frac{\{H_n\}}{n^2}$

summation contest-math harmonic-numbers

Prove that $\lim_{a \to \infty} \sum_{n=1}^{\infty} \frac{(n!)^a}{n^{an}} = 1$.

real-analysis calculus sequences-and-series limits summation

Interesting property related to the sums of the remainders of integers

elementary-number-theory summation conjectures

Prove $\sum_{n=1}^\infty \text{Ci}(\pi n)=\frac{\ln(2)-\gamma}{2}$

sequences-and-series summation trigonometric-integrals

Combinatoric formula summing one

probability combinatorics summation binomial-coefficients game-theory

Evaluation of $ \sum_{k=0}^n \cos k\theta $

trigonometry summation trigonometric-series

Prove that $0!+1! + 2! + 3! + ..... + n!$ $\neq$ $p^\text{r}$, where $n \geqslant 3$ and $n$, $p$ and $r$ are three integers

real-analysis sequences-and-series number-theory summation factorial

Experimental identities with Fibonacci series

real-analysis sequences-and-series number-theory summation fibonacci-numbers