Find the generalized sum of $1+2(2)+3(2)^2+4(2^3)+...+n(2^{n-1})$
101017
What is the sum of $\sum\limits_{i=1}^{n}ip^i$?
136066
Find the sum $\sum _{n=1}^{\infty }\left(\sqrt{n+2}-2\sqrt{n+1}+\sqrt{n}\right)$
60902
Find general solution for the equation $1 + 2 + \cdots + (n − 1) = (n + 1) + (n + 2) + \cdots + (n + r) $
103840
Calculate $\sum_{k=1}^n k2^{n-k}$
122445
Sum of the series:$\frac{1}{1\cdot 2}+\frac{1\cdot3}{1\cdot2\cdot3\cdot4}+\cdots$
62271
Find the sum of the series: $\cos^3 \alpha +\cos^3 {3\alpha} + \cos^3 {5\alpha}+....+\cos^3 {(2n-1)\alpha}$.
81589
Find the sum of $\sum_{k=0}^{\infty} 1/[(r+2k+2)(s+2k+2)]$
133398
$g(x)=\sum_{n=0}^{\infty} \lceil {\frac{n+1}{2}} \rceil x^n$, find $g(\frac{1}{3})$
28027
Find $\sum_{k=0}^{n}4^k \binom{n}{k}$
146581
The sum of the first $n$ squares $(1 + 4 + 9 + \cdots + n^2)$ is $\frac{n(n+1)(2n+1)}{6}$
101052
Find the infinite sum $\sum_{k=1}^{\infty}\sqrt k - 2\sqrt {k + 1} + \sqrt {k + 2} $
55339
Find the sum $\sum_{n=1}^{\infty}\frac{ 1}{n^{2}(2n-1)}$
32866
How find this sum $\sum\limits_{n=0}^{\infty}\frac{1}{(3n+1)(3n+2)(3n+3)}$
114280
Computing $\sum_{n=1}^∞\frac{1}{(n+1)(n+2)(n+3)....(n+p)}$
156564
Prove the identity $\sum_{{{\underset{k-even}{k=0}}}}^{n}{n \choose k}2^{k}=\frac{3^{n}+(-1)^{n}}{2}$
26446
Find the sum : $\displaystyle\sum_{i=0}^n \frac{2^i}{1+x^{2^{i}}}$
117843
Finding the sum of series $\sum_{n=0}^∞ \frac{2^n + 3^n}{6^n}$