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The Numberphile people do explain the 1/2 result

Z = 1 - 1 + 1 - 1 + 1 - 1 ......
1 - Z = 1 -[ 1 - 1 + 1 - 1 + 1 - 1 ....... ] = 1 - 1 + 1 - 1 ..... = Z
1 - Z = Z
2Z = 1
Z = 1/2

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