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

$$1+2+3+4+5+...\mathrm{\infty }=???$$

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

$$S=1+2+3+4+5+6+7+....$$$$4S=4+8+12$$$$-3S=1-2+3-4+5-6+....$$$$-3S=\frac{1}{4}$$$$S=-\frac{1}{12}$$$$⊛$$$$S=1+2+3+4+5+6+7+8+9+...$$$$S=1+(2+3+4)+(5+6+7)+(8+9+10)+...$$$$S=1+9+18+27+....$$$$S=1+9(1+2+3+4+....)$$$$S=1+9S$$$$S=-\frac{1}{8}$$$$⊛S=1+(1+1)+(1+1+1)+....$$$$S=1+(1+1)+.....$$$$......$$$$subtracting$$$$0=1+1+1+1+1+....$$$$$$

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

$$\mathrm{thank}\mathrm{you}\mathrm{so}\mathrm{much}\mathrm{sir}.$$

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

$$Butitisnottherealone.ItonlyworksinQuantumworld$$$$Itisdivergent$$

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