Is it possible to evaluate $\sum_{r=1}^{20}\frac{1}{r(r+1)}$ using $\sum_{r=1}^{n}\frac12n(n+1)$
129860
Find a formula for this sequence (and prove it).
16967
Sum : $\sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)^3}$
135927
Calculating $\sum_{n=1}^\infty\frac{1}{(n-1)!(n+1)}$
140877
Evaluate the sum $\sum_{k=1}^n {n \choose k-1} {n \choose k}$
78473
Showing $ \sum_{n=0}^{\infty} \frac{1}{(3n+1)(3n+2)}=\frac{\pi}{3\sqrt{3}}$
55061
Evaluating the sum after reordering an infinite series $1-\frac {1} {2}+\frac {1} {3}-\frac {1} {4}+\ldots $
153989
How to evaluate the sum $\frac{1}{\sqrt{n}}+\frac{1}{\sqrt{2n}}+\cdots+\frac{1}{\sqrt{n^2}}$ when $n$ grows?
16143
How can I prove that $\sum_{n=1}^\infty \frac{1}{n(n+1)} = 1$?
63474
Showing $\sum_{i = 1}^n\frac1{i(i+1)} = 1-\frac1{n+1}$ without induction?
43903
Find the sum for $\sum_{n=1}^{\infty}(-1)^{(n+1)}\frac{2n+1}{3^n} $
121554
Finding $\sum\frac{1}{2^n(n+1)}$
42271
Infinite Series $1+\frac12-\frac23+\frac14+\frac15-\frac26+\cdots$
105697
How do I evaluate $\prod_{r=1}^{\infty }\left (1-\frac{1}{\sqrt {r+1}}\right)$?
91316
Sum of the series $\sum _{ r=1 }^{ \infty }{ \frac { { r }^{ 3 } }{ r! } } $
13085
Evaluate $ 1 + \frac{1}{3}\frac{1}{4}+\frac{1}{5}\frac{1}{4^2}+\frac{1}{7}\frac{1}{4^3}+\dots$
99420
Compute $\sum_{n=1}^\infty \frac{1}{(n+1)\sqrt[]{n}+n\sqrt[]{n+1}}$
104646
Question on simplification of $\sum_{n=1}^{\infty}\frac{2}{(2n+1)(2n+3)}$?