Background :
I hope we all know that 1+2+3+4+... is an infinite sum whose solution is arguably unknown or infinity. In essence, the sum of all natural numbers from 1 to infinity is known to be unknown according to some mathematicians and even from common sense.
However, it can be shown mathematically without ambiguity (with applications from String theory and Physics) that the sum of all natural numbers is -1/12.🤔
Hence, the sum of positive integers or natural number can be shown mathematically without any debate or disrepute that it will converge to -1/12 which is even a negative fraction. How possible? Try your hands on it to prove that for a handsome price.
With the power of mathematics, this impossibility can be made possible without any doubt. Don't be surprised, it can be shown with basic algebra and mathematical manipulations.☺️
PROOF TO MY MATHEMATICAL CHALLENGE:
Embrace the power of mathematics- Maths is fun!!!😀😀👌
Background question:
Even though, S= 1+2+3+4+... is an infinite sum whose solution is arguably unknown or infinity;
We want to use a simple, but extremely smart algebraic manipulations to prove that this infinite sum
S=1+2+3+4+5+... = -1/12
which sounds very fascinating. See my solution to this mathematical challenge and follow each step.
Reminder: Even non-mathematics and maths-phobia guys can easily understand this proof as I used simple mathematical logic and algebra. See attached solution:
(NB: A more complex alternative using the Zeta function regularization and Ramanujan Summation- from String theory can be used).
Attached is a picture of the second part of the main proof using simple/basic algebraic manipulations.
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