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Question Number 108609 by Rio Michael last updated on 18/Aug/20

1 + 2 + 3 + 4 + 5 + \dots \infty = ? ? ?

Commented by ajfour last updated on 18/Aug/20

S_{n} = \frac{n (n + 1)}{2}

Answered by Dwaipayan Shikari last updated on 18/Aug/20

S = 1 + 2 + 3 + 4 + 5 + 6 + 7 + \dots .

4 S = 4 + 8 + 12

- 3 S = 1 - 2 + 3 - 4 + 5 - 6 + \dots .

- 3 S = \frac{1}{4}

S = - \frac{1}{12}

⊛

S = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + \dots

S = 1 + (2 + 3 + 4) + (5 + 6 + 7) + (8 + 9 + 10) + \dots

S = 1 + 9 + 18 + 27 + \dots .

S = 1 + 9 (1 + 2 + 3 + 4 + \dots .)

S = 1 + 9 S

S = - \frac{1}{8}

⊛ S = 1 + (1 + 1) + (1 + 1 + 1) + \dots .

S = 1 + (1 + 1) + \dots . .

\dots \dots

s u b t r a c t i n g

0 = 1 + 1 + 1 + 1 + 1 + \dots .

Commented by Rio Michael last updated on 18/Aug/20

thank you so much sir .

Commented by Dwaipayan Shikari last updated on 18/Aug/20

B u t i t i s n o t t h e r e a l o n e . I t o n l y w o r k s i n Q u a n t u m w o r l d

I t i s d i v e r g e n t