Show that arithmetic mean of numbers obtained is $\frac{n+1}{r+1}$
86902
Consider the smallest number in each of the $n\choose r$ subsets (of size $r$) of $S=\{1,2,\ldots,n\}$...
60031
Showing $\sum\limits_{j=0}^M \frac{M \choose j}{N+M \choose j} = \frac{N+M+1}{N+1}$
120093
Proof of inequality $2(\sqrt{n+1}-\sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n} - \sqrt{n-1})$ using induction
76319
How to prove $\sum\limits_{r=0}^n \frac{(-1)^r}{r+1}\binom{n}{r} = \frac1{n+1}$?
135380
Show that $\sum_{n=1}^\infty \frac{n^2}{(n+1)!}=e-1$
111353
Show that $\{a_n\}$ defined by $a_{n+1}=\frac{a_n+2}{a_n+1}$ converges
63474
Showing $\sum_{i = 1}^n\frac1{i(i+1)} = 1-\frac1{n+1}$ without induction?
14064
Proof by induction that $\sum_{i=1}^n \frac{i}{(i+1)!}=1- \frac{1}{(n+1)!}$
66210
Prove that $z^n + 1/{z^n}$ is a rational number
50972
Prove that $\sum_{x=1}^{n} \frac{1}{x (x+1)(x+2)} = \frac{1}{4} - \frac{1}{2 (n+1) (n+2)}$
96961
A proof for the identity $\sum_{n=r}^{\infty} {n \choose r}^{-1} = \frac{r}{r-1}$
16143
How can I prove that $\sum_{n=1}^\infty \frac{1}{n(n+1)} = 1$?
126105
Compute $\sum_{k=1}^{n} \frac 1 {k(k + 1)} $
153226
Proof of $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
76290
arithmetic mean of a sequence converges
73938
Prove that $\sum_{r=1}^nr(r+1)=\frac{n(n+1)(n+2)}{3}$ using induction
13323
Convergence of the arithmetic mean