New posts in Telescopic Series

Prove that inequality $1+\frac{1}{2\sqrt{2}}+...+\frac{1}{n\sqrt{n}}<2\sqrt{2}$

Find the value of $S$ in term of $k$ (telescoping sums)

What is $x$, if $\cot ^{-1} \left(3x+\frac{2}{x}\right)+\cot ^{-1} \left(6x+\frac{2}{x}\right)+\cot ^{-1} \left(10x+\frac{2}{x}\right)+\cdots = 1$?

Find $\sum_{k=1}^\infty\frac{1} {k(k+1)(k+2)(k+3)}$

If $|x_{n+1} - x_n| < \epsilon,$ is $(x_n) $ a Cauchy sequence?

How to evaluate the sum : $\sum_{k=1}^{n} \frac{k}{k^4+1/4}$

Telescoping(?) an infinite series

Computing $\sum\limits_{n=1}^q {1\over (kn-1)(kn)(kn+1)}$ as a telescoping series, when $k\geqslant3$?

How to solve $\sum_{k=1}^\infty \frac{1}{(2k-1)(2k+1)}$

What is the formula for $\frac{1}{1\cdot 2}+\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\cdots +\frac{1}{n(n+1)}$