If you look at the series:
S = 1 – 1 + 1 -1 + 1 -1 …to infinity
the sum turns out to be , S=0.
Now , if we look it in another way
S = 1 -(1-1) – (1-1) – (1-1)…to infinity
the Sum turns out to be , S=1
The result is either 0 or 1.
The most interesting part comes now.
A priest and Mathematician named Grandi, presented an alternate but mind boggling proof for the summation.
Let us say ,
S = 1-1+1-1+1-1…
S = 1-(1-1+1-1+1 …)
So that makes it,
2S = 1
The most fun part is the result , sum of all the integers being a fraction (1/2).
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