Formula for $r+2r^2+3r^3+...+nr^n$
6416
How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?
94580
Prove that, $\binom{3n}{r}=\binom{3n-1}{r} + \binom{3n-1}{r-1}$
634
Closed form formula for $\sum\limits_{k=1}^n k^k$
89698
Please help with $\sum\limits_{r=1}^{N}\frac{2r+3}{3^r(r+1)}$
58633
Proof of the formula $1+x+x^2+x^3+ \cdots +x^n =\frac{x^{n+1}-1}{x-1}$
113189
Find the sum of the series $1^2-2^2+3^2-4^2+...-(2n)^2$
39659
Is there a closed formula for this summation?
7073
How to get to the formula for the sum of squares of first n numbers?
29524
Formula for the sum $\sum_{i=2}^{n} \frac1{i^2-1}$
114506
Expansion of $(1+\sqrt{2})^n$
7066
Calculate simple expression: $\sqrt[3]{2 + \sqrt{5}} + \sqrt[3]{2 - \sqrt{5}}$
27756
Find a formula for a sequence $\{\sqrt{3},\sqrt{3\sqrt{3}},\sqrt{3\sqrt{3\sqrt{3}}},...\}$
85653
$2^x + 3^x - 4^x + 6^x - 9^x ≤ 1$ $\forall x \in R$
92810
What is $\sum_{r=1}^\infty\frac{r+2}{2^{r+1}(r)(r+1)}$?
103840
Calculate $\sum_{k=1}^n k2^{n-k}$
1158
How to prove this binomial identity $\sum_{r=0}^n {r {n \choose r}} = n2^{n-1}$?
56624
Prove that $0!+1! + 2! + 3! + ..... + n!$ $\neq$ $p^\text{r}$, where $n \geqslant 3$ and $n$, $p$ and $r$ are three integers