Show ($n+1$)$2^n$ = $\sum_{i\geq 0}^{} {n + 1\choose i}i$ algebraically.
1158
How to prove this binomial identity $\sum_{r=0}^n {r {n \choose r}} = n2^{n-1}$?
10211
Proving that $\sum\limits_{k=0}^{n} {{m+k} \choose{m}} = { m+n+1 \choose m+1 }$
148442
Show that the sum $\sum_{k = 0}^n 2^k \binom{n}{k}$ is equal to $3^n$
25826
Proof of a combinatorial identity: $\sum\limits_{i=0}^n {2i \choose i}{2(n-i)\choose n-i} = 4^n$
147910
Prove that $\sum_{n=0}^N\binom{2N-n}N2^n(n+1)=(1+2N)\binom{2N}N$
150642
How to prove $\sum^n_{i=1} \frac{1}{i(i+1)} = \frac{n}{n+1}$?
44161
Using induction to prove $\sum_{k=0}^{N-1} 2^k = 2^N-1$
57780
$\sum_{i=1}^n i\cdot i! = (n+1)!-1$ By Induction
120976
Proving $\sum_{k=0}^{n}k{n\choose k}^2 = n{2n-1 \choose n-1} $
66568
Number Theory : Show that $\sum_{i=0}^\infty$ $ [\frac{n}{2^i}+\frac{1}{2}]$ $=$ $2n$
86896
Prove by induction. How do I prove $\sum\limits_{i=0}^n2^i=2^{n+1}-1$ with induction?
100361
Show that ord$_{p}2 = 2^{n + 1}$.
14435
Show by induction: $(1+\frac{1}{n})^{n}<n$
6539
Prove $\sum_{i=1}^n i! \cdot i = (n+1)! - 1$?
151757
Simplify $\sum_{i=0}^{N/2}{N-i\choose i}$
58247
Prove $\sum_{k=0}^n \binom{n+k}{k}=\binom{2n+1}{n}$
29828
Combinatorial proof of $\sum^{n}_{i=1}\binom{n}{i}i=n2^{n-1}$.