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Summary: How to Add Divergent Series
Abstract
In string theory, we have to calculate 1 + 2 + 3 + · · · = - 1
12.
"Divergent series are on the whole devil's work, and it is a shame that one
dares to found any proof on them. One can get out of them what one wants
if one uses them, and it is they which have made so much unhappiness and so
many paradoxes. Can one think of anything more appalling than to say that
0 = 1 - 2n
+ 3n
- 4n
+ . . .
where n is a positive number. Here's something to laugh at, friends." - Niels
Henrik Abel (1826)
1 1 + 2 + 3 + 4 + . . .
A Use the derivative of geometric series
1 + 2x + 3x2
+ . . . =
d
dx
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