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Question Number 104173 by Dwaipayan Shikari last updated on 19/Jul/20

$$\mathrm{For}\mathrm{fun}!$$$${\mathrm{S}}_{\mathrm{n}}=1+2+3+4+5+6+7+...$$$${2\mathrm{S}}_{\mathrm{n}}=2+4+6+..$$$$-{\mathrm{S}}_{\mathrm{n}}=1+3+5+7+9+11+.....$$$$-(-\frac{1}{12})=1+3+5+7+9+11+...$$$$1+3+5+7+9+....=\frac{1}{12}$$$$$$$${\mathrm{S}}_{\mathrm{n}}=1+2+3+4+5+6+7+....$$$${\mathrm{S}}_{\mathrm{n}}=1+(1+1)+(1+2)+(1+3)+...$$$${\mathrm{S}}_{\mathrm{n}}=(1+1+1+....)+{\mathrm{S}}_{\mathrm{n}}$$$$1+1+1+1+1+1+....=0$$

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