How can I simplify $\sum_{k=0}^n a \cdot k \cdot q^k$?
7063
How to compute the  formula $\sum  \limits_{r=1}^d r \cdot 2^r$?
125712
Working with binomial coefficient $\sum_{k=0}^n (-1)^k \binom nk=0$
47670
Algebraic proof of $\sum_{i=0}^k{{n \choose i}{m \choose {k-i}}}= {{m+n}\choose k}$
3356
Why $\sum_{k=0}^m x^k $ is equal to $\dfrac{x^{m+1}-1}{x-1} $?
110996
Sum of the form $r+r^2+r^4+\dots+r^{2^k} = \sum_{i=1}^k r^{2^i}$
562
Formula for calculating $\sum_{n=0}^{m}nr^n$
107071
Prove $\sum_{k= 0}^{n} k \binom{n}{k} = n \cdot 2^{n - 1}$ using the binomial theorem
116722
Simplifying $\big(\sum_{i=0}^n\binom{k}{i}\binom{M-k}{n-i}\frac{k-i}{M-n}\big)/{\binom{M}{n}}$
58428
Proving $\sum_{k=0}^{n} {k \choose a} {n-k \choose b} = {n+1\choose a+b+1}$
146305
Simplify sum of factorials with mathematical induction
133905
Intuitive proof of $\sum_{k=1}^{n} \binom{n}{k} k^{k-1} (n-k)^{n-k} = n^n$
30518
Formula for $\sum_{k=1}^n \frac{1}{k(k+1)(k+2)}$?
7302
$\sum k! = 1! +2! +3! + \cdots + n!$ ,is there a generic formula for this?
99843
How to simplify $ \sum_{k=0}^{\infty} \binom{k + r - 1}{k} x^k$
51842
Simplify $\prod_{k=1}^5\tan\frac{k\pi}{11}$ and $\sum_{k=1}^5\tan^2\frac{k\pi}{11}$
14197
show that $\sum_{i=0}^l \dfrac{{l\choose i}}{{n\choose k + i}} = \dfrac{n+1}{(n-l+1) {n-l\choose k}}$
5049
Proving $\sum_{k=0}^n(-1)^k\binom nk=0$