Formula for $\sum_{k=1}^n k2^k$
6416
How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?
37771
Sum of a power series $n x^n$
117837
Formula for the general Cavalieri Sum: $S_n(p)=\sum\limits_{k=1}^{n} k^p\,\,\,n, p\in\mathbb N$
118372
Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$
29524
Formula for the sum $\sum_{i=2}^{n} \frac1{i^2-1}$
94927
Can we calculate $2^k$ using this easy Taylor series?
14239
How to show $\sum_{k=0}^{n}\binom{n+k}{k}\frac{1}{2^k}=2^{n}$
44161
Using induction to prove $\sum_{k=0}^{N-1} 2^k = 2^N-1$
61547
Derive an explicit formula for a power series $\sum_{n=1}^\infty n^2x^n$
151179
Finding the value of $\sum k/3^k$
114173
Explanation of the formulas for sums $\sum nr^n$ and $\sum n^2 r^n$
42831
How to derive the formula for the sum of the first $n$ odd numbers: $n^2=\sum_{k=1}^n(2k-1).$
151085
Simplify the sum $ \sum_{i=0}^{k}(-1)^i i \binom{n}{i} \binom{n}{k-i}$
44111
Find the value of $\sum_{k=1}^{n}k\binom{n}{k}$?
7302
$\sum k! = 1! +2! +3! + \cdots + n!$ ,is there a generic formula for this?
36361
How to calculate the summation $(\sum_{p = k}^{n} \binom{n}{p}) / 2^n$ quickly?
14399
Calculate $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k}$