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There is another way to show that the sum of 1-1+1-1... = 1/2, and it’s by first considering the binomial expansion of 1/(1+x), or (1+x)^-1. When you expand, you get 1-x+x²-x³..., and if you substitute in x=1, this turns into 1-1+1-1... Substitutimg x=1 into the original fraction 1/1+x which we expanded then gives us 1/2.