- #1

MevsEinstein

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- TL;DR Summary
- I used some Calculus and the Ramanujan sum to make this proof.

After learning about this formula for the sum of increasing powers - ##1+p+p^2+p^3+...=1/(1-p)## - I decided to differentiate both sides of the equation, getting: ##1+2p+3p^2+4p^3+...=1/((1-p))^2##. Substituting ##1## for ##p##, I get: ##1+2+3+4+...=1/0##. But Ramanujan said that ##1+2+3+4+...=-1/12##, so ##1/0=1/-12##, meaning ##0=-12##, meaning ##0=1## (dividing both sides by ##-12##). There MUST be something wrong about this proof, since ##0## is NOT equal to one. May someone help me find the fallacy?

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