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
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









