$1+2+3+4+5+\dotsb =\frac{-1}{12}$ Is this true in real domain? Can you tell where this series is used?
4340
Why does $1+2+3+\cdots = -\frac{1}{12}$?
23576
Calculating $1+\frac13+\frac{1\cdot3}{3\cdot6}+\frac{1\cdot3\cdot5}{3\cdot6\cdot9}+\frac{1\cdot3\cdot5\cdot7}{3\cdot6\cdot9\cdot12}+\dots? $
67434
Finding the infinite series: $3 \cdot \frac{9}{11} + 4 \cdot \left(\frac{9}{11}\right)^2 + 5 \cdot \left(\frac{9}{11}\right)^3 + \cdots$?
12812
Sum of the alternating harmonic series $\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{k} = \frac{1}{1} - \frac{1}{2} + \cdots $
76387
Evaluate the series $\sum_{n=1}^{\infty} \frac{2^{[\sqrt{n}]}+2^{-[\sqrt{n}]}}{2^n}$
41645
Checking my understanding: $1 - 1 + 1 - 1 + 1 - ... = \frac{1}{2}$
111705
Why does $\frac{1+t}{(1-t)^3}=\sum_{n=0}^{\infty}(1+n)^2t^n$
42271
Infinite Series $1+\frac12-\frac23+\frac14+\frac15-\frac26+\cdots$
100936
What is the sum of this series: $\frac{2}{\pi}\sum_{k=1}^{\infty}\frac{(-1)^{k-1}}{2k-1}$
113189
Find the sum of the series $1^2-2^2+3^2-4^2+...-(2n)^2$
13085
Evaluate $ 1 + \frac{1}{3}\frac{1}{4}+\frac{1}{5}\frac{1}{4^2}+\frac{1}{7}\frac{1}{4^3}+\dots$
40464
Find series representation of a function $ y=\frac{1}{1+x+x^{2}+x^{3}} $
99542
Does the series $1 + \frac{1}{2} - \frac{1}{3} + \frac{1}{4} + \frac{1}{5} - \frac{1}{6} + \dots$ converge?
124248
$1+\frac {1}{4}(1+\frac {1}{4}) +\frac {1}{9}(1+\frac {1}{4} +\frac {1}{9})+....$
40534
What is $(-1)^{\frac{2}{3}}$?
136444
Evaluating $\sum_{n=0}^\infty\frac{(-1)^n}{3n+1}$
22636
Find the sum of the series $\sum \limits_{n=1}^{\infty} \frac{2^{-n}(n+3)}{(n+1)(n+2)}$