1/3+1/6+1/12+1/24+…… +1/3*2^n-1+…… = ditto

s=1/3+1/6+1/12+1/24+…… +1/3*2^n-1 s=2s-s=(2/3+1/3+1/6+...+1/3*2^n-2)-(1/3+1/6+1/12+1/24+…… +1/3*2^n-1) =2/3-1/3*2^n-1 =(2^(n) -1)/3*2^(n-1)

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