Find $\sum\frac{a(n)}{n(n+1)}$, where $a(n)$ --- number of 1's in binary expansion of n.
140843
How does one [easily] calculate $\sum\limits_{n=1}^\infty\frac{\mathrm{pop}(n)}{n(n+1)}$?
122534
Show that $\sum (-1)^{n+1}/n$ = $k$ can be expanded to a sum with $ 1 - 1/2 + 1/3 + 1/5 - 1/4 +1/7 + 1/9 - 1/6 + ....$ which is $3k/2$
30851
Find the summation $\frac{1}{1!}+\frac{1+2}{2!}+\frac{1+2+3}{3!}+ \cdots$
69498
What is $\sum_{r=0}^n \frac{(-1)^r}{\binom{n}{r}}$?
18796
How to find the sum of the series $1+\frac{1}{2}+ \frac{1}{3}+\frac{1}{4}+\dots+\frac{1}{n}$?
74117
Find the sum of series $\sum_{n=0}^{\infty}\frac{z^{kn}}{(kn)!}$
99003
How do we calculate this sum $\sum_{n=1}^{\infty} \frac{1}{n(n+1)\cdots(n+p)}$?
25504
How to find sum of the infinite series $\sum_{n=1}^{\infty} \frac{1}{ n(2n+1)}$
33986
Calculate $\sum_{n=1}^{\infty}(\frac{1}{2n}-\frac{1}{n+1}+\frac{1}{2n+4})$
97656
Finding $a_n$ if $a_0=a_1=1,a_{n+1}=n(a_n+a_{n-1})\ \ (n\ge 1).$
93427
Show that $\sum_{i=1}^{n} \frac {a_i}{1+a-a_i} + \prod_{i=1}^{n} {(1-a_i)} \leq 1$
71824
Finding the sum of the series $\frac{1}{1!}+\frac{1+2}{2!}+\frac{1+2+3}{3!}+ \ldots$
3341
Find $\sum_{r=1}^{3n-1}{ (-1)^{r-1}r\over{3n \choose r}}$, if $n$ is even
96945
General formula of $\sum_{n\ge1}{\binom{2n}{n}^{-k}}$.
107179
Partial fraction expansion of $\frac{1}{x(x+1)(x+2)\cdots(x+n)}$
142303
Alternating sum of binomial coefficients multiplied by (1/k+1)
92440
Let $n \in \mathbb{Z}^+$, prove the identity $ \sum_{k=1}^{n-1} \binom {n} {k} \frac{kn^{n-k}}{k+1}=\frac{n(n^{n}-1)}{n+1}$