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In response to
"1 + 2 + 3 + 4 + ... = -1/12 -- nm"
by
Apple Baron Betty 🥧
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Proof! Reagen, blow your students minds with this.
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Prep work:
A = 1 - 1 + 1 - 1 + 1 - 1 + ...
A = 0 + 1 - 1 + 1 - 1 + 1 - ...
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2A = 1
A = 1/2
B = 1 - 2 + 3 - 4 + 5 - 6 + ...
B = 0 + 1 - 2 + 3 - 4 + 5 - ...
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2B = 1 - 1 + 1 - 1 + 1 - 1 + ... (A above)
2B = 1/2
B = 1/4
Goal:
C = 1 + 2 + 3 + 4 + 5 + 6 + ...
-4C = 0 - 4 + 0 - 8 + 0 - 12 + 0 - 16 + ...
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-3C = 1 - 2 + 3 - 4 + 5 - 6 + ... (B above)
-3C = 1/4
C = -1/12
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