Having trouble understanding why $\sum_{i=1}^ni^2= \frac{n(n+1)(2n+1)}{6}$
16472
Sum of First $n$ Squares Equals $\frac{n(n+1)(2n+1)}{6}$
127267
Evaluation of $\sum_{n=1}^{\infty}\frac{1}{n(2n+1)}=2-2\ln(2)$
98808
Finite Sum $\sum_{i=1}^n\frac i {2^i}$
118571
Why is $\sum\limits_{k=0}^{n}(-1)^k\binom{n}{k}^2=(-1)^{n/2}\binom{n}{n/2}$ if $n$ is even?
5272
Proving that $\sum_{k=0}^{n}\frac{(-1)^k}{{n\choose k}}=[1+(-1)^n] \frac{n+1}{n+2}.$
60031
Showing $\sum\limits_{j=0}^M \frac{M \choose j}{N+M \choose j} = \frac{N+M+1}{N+1}$
153231
Why does $\sum_1^\infty \frac1{n^3}=\frac52\sum_1^\infty\frac{(-1)^{n-1}}{n^3\binom{2n}{n}}$?
120976
Proving $\sum_{k=0}^{n}k{n\choose k}^2 = n{2n-1 \choose n-1} $
89771
$\frac{1}{s-1}+\sum_{n=1}^{\infty}\left[\frac{1}{n^s}+\frac{1}{s-1}\left(\frac{1}{(n+1)^{s-1}} - \frac{1}{n^{s-1}}\right)\right]$
96039
Why is $\frac {1\cdot2\cdot3\cdot...\cdot n}{(n+1)(n+2)...(2n)}\le \frac 1 {n+1}$
114414
Sum of $\sum_{k=1}^n\sin{k\theta}$
44970
Show $\sum_{n=0}^\infty\frac{1}{a^2+n^2}=\frac{1+a\pi\coth a\pi}{2a^2}$
43903
Find the sum for $\sum_{n=1}^{\infty}(-1)^{(n+1)}\frac{2n+1}{3^n} $
93690
How to obtain the sum of the following series? $\sum_{n=1}^\infty{\frac{n^2}{2^n}}$
39909
Getting a closed form from $\sum_{i=1}^{n-1} \sum_{j=i+1}^{n} \sum_{k=1}^{j} 1$
53116
How find this sum $f(n)=\sum_{i=1}^{n}\dfrac{\binom{n}{i}}{i}$
73938
Prove that $\sum_{r=1}^nr(r+1)=\frac{n(n+1)(n+2)}{3}$ using induction