1 = 1

1 = (-1) + 2

1 = (-2) + 3

1 = (-3) + 4

1 = (-4) + 5 ... And so on...

By adding term by term to all these equations, we get: 1 + 1 + 1 + 1 + 1 + 1 + ... = 1 + (-1) + 2 + (-2) + 3 + (-3) + 4 + (-4) + 5 + ...

In the expression on the right, all the terms cancel out in pairs, giving: 1 + 1 + 1 + 1 + 1 + 1 + ... = 0

The expression on the left, consisting of an infinite sum of terms equal to 1, tends to infinity. Thus, 0 is equal to infinity.

And yet 0 is not equal to infinity. So where is the mistake?

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[–] 7 points 3 months ago* (last edited 3 months ago)

1 + 1 + 1 + 1 + 1 + 1 + … = 1 + (-1) + 2 + (-2) + 3 + (-3) + 4 + (-4) + 5 + …

You forgot -5+6 on purpose.

spoiler
"In the expression on the right, all the terms cancel out"

You forgot the last one which is equal to the sum on the left.

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