Simplifying $\sum_{i=1}^{n-2}i(n-1-i)$
11612
How to show that $\sum_{k=1}^n k(n+1-k)=\binom{n+2}3$?
110996
Sum of the form $r+r^2+r^4+\dots+r^{2^k} = \sum_{i=1}^k r^{2^i}$
118372
Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$
124135
A general formula for $\sum (k-1)(k-2)(k-3)$?
23726
A closed form for $1^{2}-2^{2}+3^{2}-4^{2}+ \cdots + (-1)^{n-1}n^{2}$
63474
Showing $\sum_{i = 1}^n\frac1{i(i+1)} = 1-\frac1{n+1}$ without induction?
143365
Is $\sum_{i=1}^{n-1}i=\binom{n}{2}$?
19581
$\sum_{k=0}^n (-1)^k \binom{n}{k}^2$ and $\sum_{k=0}^n k \binom{n}{k}^2$
86900
Formula for the $1\cdot 2 + 2\cdot 3 + 3\cdot 4+\ldots + n\cdot (n+1)$ sum
84147
Evaluating $\sum_{n=1}^\infty \frac{2^{2n-1}}{5^{n+1}}$
74294
How to simplify $\sum_{i=1}^{k}\binom{n + i - 1}{i}$?
34374
Simplifying factorials: $\frac{(n-1)!}{(n-2)!}$
67271
$\sum_{n=-\infty}^{\infty}\frac{1}{(u +n)^2}=\frac{\pi^2}{(\sin \pi u)^2}$
107433
Prove the sum to n terms of the series
100971
How to simplify the series of $x + x^{-1} + (x + x^{-1})^{-1} + (x + x^{-1} + (x + x^{-1})^{-1})^{-1}$?
156720
Evaluate $\sum_ {n=1}^{\infty} \cot^{-1}(2n^2)$
146305
Simplify sum of factorials with mathematical induction