1/2+3/4+7/8+15/16……+2^(100-1)/2^100
热心网友
S = 1/2 + 3/4 + 7/8 + 15/16 +………+ 2^(100-1)/2^100 设T = 1/2 + 1/4 + 1/8 + 1/16 +………+1/2^100则T为等比数列，公比为1/2，所以T = 1/2 + 1/4 + 1/8 + 1/16 +………+1/2^100 = (1/2)[1 - (1/2)^100]/(1 - 1/2) = 1 - (1/2)^100(S + T) = (1/2 + 1/2) + (3/4 + 1/4) + ……… + [2^(100-1)/2^100 + 1/2^100] = 1×100 = 100S = (T + S) - T = 100 - [1 - (1/2)^100] = 99 + (1/2)^100 即：1/2 + 3/4 + 7/8 + 15/16 +………+ 2^(100-1)/2^100 = 99 + (1/2)^100。
热心网友
误解为0
热心网友
K=1/2+1/4+1/8+1/16+..........+1/2^100=1-(1/2)^100等比数列原式=100-K=99+(1/2)^100