New posts in Summation

Why this inequality is correct

prove that $\sum_{cyc}\frac{a}{b^2+c^2}\ge \frac{4}{5}\sum_{cyc}\frac{1}{b+c}$

If $x+y+z=xyz$, prove $\frac{2x}{1-x^2}+\frac{2y}{1-y^2}+\frac{2z}{1-z^2}=\frac{2x}{1-x^2}\times\frac{2y}{1-y^2}\times\frac{2z}{1-z^2}$

Proving inequality: $\sum_{i=1}^n \left(a_i^7+a_i^5\right) \geq 2(\sum_{i=1}^n a_i^3)^2$

summing this binomial series

Evaluating $\sum_{n=k}^{\infty} \frac{1}{ \binom{n}{k}}$

Finding $\sum_{n=1}^{\infty} \frac{1}{f(n)}$ where $f$ is a real quadratic function?

Prove $\sum_{m=i}^{n}2^{n-m}\binom{m}{i}=\binom{n+1}{i+1}+\ldots+\binom{n+1}{n+1}=\sum_{m=i}^{n}\binom{n+1}{m+1}$ without induction

Does $\Im(e^i+e^{e^i}+e^{e^i+e^{e^i}}\dots)$ converge?

Sum of Telescopic Series