Proof that $\sum_{n=1}^\infty n $ is -1/12
4340
Why does $1+2+3+\cdots = -\frac{1}{12}$?
147165
Does the fact that $\sum_{n=1}^\infty 1/2^n$ converges to $1$ mean that it equals $1$?
57759
Determining the infinite sum $\sum\limits_{n=0}^{\infty}\frac{(-1)^n}{2n+1}$
150148
Sum of $\sum^\infty_{n=2} \frac{1}{\ln{(n!)}}$
4253
How to calculate: $\sum_{n=1}^{\infty} n a^n$
34496
Proof that $e=\sum\limits_{k=0}^{+\infty}\frac{1}{k!}$
128913
A proof of $\sum_{i=1}^{n}(-1)^{i-1}\binom{n}{i}\frac{1}{i}=\frac{1}{1}+\frac{1}{2}+....+\frac{1}{n}$
24373
Hint on computing the series $\sum_{n=2}^\infty \frac{1}{n^2-1}$.
127267
Evaluation of $\sum_{n=1}^{\infty}\frac{1}{n(2n+1)}=2-2\ln(2)$
63968
How to prove that $\lim\limits_{n\rightarrow \infty} \frac{1}{n^2}\sum\limits_{k=1}^{n}(n \bmod k)=1-\frac{\pi^2}{12}$?
5272
Proving that $\sum_{k=0}^{n}\frac{(-1)^k}{{n\choose k}}=[1+(-1)^n] \frac{n+1}{n+2}.$
127537
Is there any mathematical or physical situations that $1+2+3+\ldots\infty=-\frac{1}{12}$ shows itself?
96961
A proof for the identity $\sum_{n=r}^{\infty} {n \choose r}^{-1} = \frac{r}{r-1}$
139229
How to prove by arithmetical means that $\sum\limits_{k=1}^\infty \frac{((k-1)!)^2}{(2k)!} =\frac{1}{3}\sum\limits_{k=1}^{\infty}\frac{1}{k^{2}}$
9960
Sum of an infinite series $(1 - \frac 12) + (\frac 12 - \frac 13) + \cdots$ - not geometric series?
140614
Show that $\sum^\infty_{n=m}\frac{1}{n^2} = O(\frac{1}{m})$
725
proof of $\sum_{n=1}^\infty n \cdot x^n= \frac{x}{(x-1)^2}$