How do I prove this equality $\displaystyle \sum_{k=0}^n \frac{1}{k+1}\text{C}_n^k=\frac{2^{n+1}-1}{n+1}$?
61270
Binomial Theorem Sum
86567
Understanding $\sum_{x = 0}^y x = \frac{y(y + 1)}{2}$ in a step of a proof
64378
Proving a binomial sum identity $\sum _{k=0}^n \binom nk \frac{(-1)^k}{2k+1} = \frac{(2n)!!}{(2n+1)!!}$
139430
How to prove that $\sum_{n=1}^{+\infty}\frac{1}{n^2+1}=\frac{-1+\pi \coth (\pi)}{2}$?
36436
Proving $\sum_{k=1}^n k k!=(n+1)!-1$
26446
Find the sum : $\displaystyle\sum_{i=0}^n \frac{2^i}{1+x^{2^{i}}}$
5272
Proving that $\sum_{k=0}^{n}\frac{(-1)^k}{{n\choose k}}=[1+(-1)^n] \frac{n+1}{n+2}.$
15045
Proving $\sum\limits_{l=1}^n \sum\limits _{k=1}^{n-1}\tan \frac {lk\pi }{2n+1}\tan \frac {l(k+1)\pi }{2n+1}=0$
138542
Evaluating sums question $\sum_{k=2}^n \frac{1}{k^2-1}$
11612
How to show that $\sum_{k=1}^n k(n+1-k)=\binom{n+2}3$?
135380
Show that $\sum_{n=1}^\infty \frac{n^2}{(n+1)!}=e-1$
9046
Prove that $\sum_{k=0}^{m}\frac{\binom{m}{k}}{\binom{n}{k}}=\frac{n+1}{n+1-m}$
142132
How do you prove $\sum \frac {n}{2^n} = 2$?
73938
Prove that $\sum_{r=1}^nr(r+1)=\frac{n(n+1)(n+2)}{3}$ using induction
32791
Proving this binomial identity $\sum_{k=0}^n {n+k \choose k} \frac{1}{2^{k}}= 2^{n}$
63553
Show that $\frac{1}{(n+1)!}(1+\frac{1}{(n+1)}+\frac{1}{(n+1)^2}+\frac{1}{(n+1)^3}+\cdots)=\frac{1}{n!n}$
82742
Proving that ${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $