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证明:1+2+3+…… = -1/12

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设:a = 1-1+1-1+1-1+……
则:2a = 1,a = 1/2
再设:
b = 1-2+3-4+5-6+……
2b = 1-1+1-1+1-1+1-1 = a,b = a/2 = 1/4
再设:
S = 1+2+3+4+5+……
b = 1-2+3-4+5-6+7……
S - b = 4+8+12+16+20+…… = 4(1+2+3+4+……) = 4S
立即可得:
- b = 3S
S = - b/3 = - 1/12


IP属地:上海1楼2026-02-19 11:38回复
    1! = 1,2!= 2,则:(1/2)! = (√π)/2


    IP属地:上海2楼2026-02-21 17:58
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