How to solve $a_{n+1}=a_n+\frac{1}{a_n}$
22077
Closed form for the sequence defined by $a_0=1$ and $a_{n+1} = a_n + a_n^{-1}$
60902
Find general solution for the equation $1 + 2 + \cdots + (n − 1) = (n + 1) + (n + 2) + \cdots + (n + r) $
326
Find $\sum_{k=1}^{\infty}\frac{1}{2^{k+1}-1}$
15985
simplify $(a_1 + a_2 +a_3+... +a_n)^m$
91000
Prove that $\frac{1}{a+1}0$
37007
Evaluating $\sum_{k=1}^{n} \frac{1}{k(k+1)}$
150642
How to prove $\sum^n_{i=1} \frac{1}{i(i+1)} = \frac{n}{n+1}$?
88782
Finding the limit of $x_1=0 , x_{n+1}=\frac{1}{1+x_n}$
9490
Let $(1+x+x^2)^n=a_0+a_1x+a_2x^2+\cdots+a_{2n}x^{2n}$ be an identity in $x$. Find $a_0 +a_2 +a_4+ \cdots +a_{2n} $ in terms of $n$
11664
If $a_0+\frac{a_1}{2}+\dots + \frac{a_n}{n+1}=0$ then $a_nx^n+\dots + a_0$ has a root in $[0,1]$
125057
How do I solve a problem with term $a^{n} + b^{n}$?
121606
How do I prove that the limit of the sequence exists: $a_n = \frac1n +\frac 1{n+1} + \frac1{n+2} + \dots + \frac1{2n}$?
111805
If $a_{1}=1$ and $a_{n+1}=1+\frac{n}{a_{n}}$, then $a_{n}=\sqrt{n}+\frac{1}{2}-\frac{1}{8\sqrt{n}}+o\left(\frac{1}{\sqrt{n}}\right)$
89728
Prove that $1<\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{3n+1}$
23315
Solve $\frac{b}{a}=a.b$ in decimal
50087
Convergence of $a_{n+1}=\frac{1}{1+a_n}$
79170
$1 + \frac{1}{1+2}+ \frac{1}{1+2+3}+ ... + \frac{1}{1+2+3+...+n} = ?$