Help with difficult telescoping series question: $\frac3{1!+2!+3!}+\frac4{2!+3!+4!}+\ldots+\frac{2012}{2010!+2011!+2012!}$
103343
Finding $\frac{3}{1!+2!+3!}+\frac{4}{2!+3!+4!} +\frac{5}{3!+4!+5!}+\cdots+\frac{2008}{2006!+2007!+2008!}$
53658
Find the sum series $\sum_{n=1}^{+\infty} \frac{(-1)^{n-1}(2n-1)}{2^{n-1}}$
76387
Evaluate the series $\sum_{n=1}^{\infty} \frac{2^{[\sqrt{n}]}+2^{-[\sqrt{n}]}}{2^n}$
79415
The series $\sum_{n=2}^{\infty }\frac{1}{\log (n!)}$
67434
Finding the infinite series: $3 \cdot \frac{9}{11} + 4 \cdot \left(\frac{9}{11}\right)^2 + 5 \cdot \left(\frac{9}{11}\right)^3 + \cdots$?
31485
Three negative and three positive $1$s in a serie
57372
Series convergence of $\sum_{n=1}^{\infty}\frac{1}{n^3}$
138172
Find the sum to n terms of the series $\frac{1}{1.2.3}+\frac{3}{2.3.4}+\frac{5}{3.4.5}+\frac{7}{4.5.6}+\cdots$..
145007
Two problems on real number series
9193
Simple series convergence/divergence: $\sum_{k=1}^{\infty}\frac{2^{k}k!}{k^{k}}$
18814
Sum of the series $1+\frac{1\cdot 3}{6}+\frac{1\cdot3\cdot5}{6\cdot8}+\cdots$
139327
Find the limit of a series of fractions starting with $\frac{1}{2}, \, \frac{1/2}{3/4}, \, \frac{\frac{1}{2}/\frac{3}{4}}{\frac{5}{6}/\frac{7}{8}}$
17492
Recurrence telescoping $T(n) = T(n-1) + 1/n$ and $T(n) = T(n-1) + \log n$
32637
What is the sum of this series: $\displaystyle\sum_{n=0}^{\infty} \dfrac{a^n}{(3n)!}$
42271
Infinite Series $1+\frac12-\frac23+\frac14+\frac15-\frac26+\cdots$
93690
How to obtain the sum of the following series? $\sum_{n=1}^\infty{\frac{n^2}{2^n}}$
91410
Finding the sum of this series: $1+\frac 12 + \frac 13 + \cdots + \frac 1{50}$