Hint to find a Closed Form of $\sum_{1 \leq k \leq n}\frac{1}{k(k+1)}$
37007
Evaluating $\sum_{k=1}^{n} \frac{1}{k(k+1)}$
50812
Partial sum of the series $\sum\limits_{r=1}^{\infty} \frac{1}{r(r+1)}$
86348
Proving $\sum\limits_{k=0}^{n-1} \Bigl[x + \frac{k}{n}\Bigr] = [nx]$
113891
The limit of a sum of the form $a_0 \sqrt n + a_1 \sqrt {n + 1} +\cdots + a_k \sqrt {n + k}$
39909
Getting a closed form from $\sum_{i=1}^{n-1} \sum_{j=i+1}^{n} \sum_{k=1}^{j} 1$
69084
What is the closed form for $\sum_{n=1}^\infty \frac1n - \frac1{n+1/p}$?
153226
Proof of $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
349
Prove $| \sum_{i \leq n} \frac{\mu(i)}{i} | \leq 1$
135218
Closed Form for Factorial Sum
60031
Showing $\sum\limits_{j=0}^M \frac{M \choose j}{N+M \choose j} = \frac{N+M+1}{N+1}$
124229
Simplify $\sum_{k=0}^{\infty} x^ky^{\frac{k(k+1)}{2}}$
36742
The sum of $(-1)^n \frac{\ln n}{n}$
121617
Closed form of $\sum_{n=0}^{\infty} \frac{\cos(\alpha \, n)}{n!}$
634
Closed form formula for $\sum\limits_{k=1}^n k^k$
133070
Finding a closed form expression for the recurrence relation $a(n,k+1)=(k+1)^n+\sum_{m=1}^k {k+1\choose m}a(n,m)$
326
Find $\sum_{k=1}^{\infty}\frac{1}{2^{k+1}-1}$
158616
A closed form for the sum $S = \frac {2}{3+1} + \frac {2^2}{3^2+1} + \cdots + \frac {2^{n+1}}{3^{2^n}+1}$ is ...