Question

问道数学题。急急急。1024+512+256......+2+1+1/2+1/4+1/8+......+1/512+1/1024 。用简便方法怎么算？

Answer 1

1024+512+256......+2+1+1/2+1/4+1/8+......+1/512+1/1024 =2^ 10+2^ 9+2^ 8......+2^ 1+2^ 0+2^ (-1)+2^ (-2)+2^ (-3)+......+2^ (-9)+2^ (-10) 这是一个等比数列求和，q=1/2，项数为11项，Sn=a1(1-q^n)/(1-q)=(a1-an*q)/(1-q) 2^ 10+2^ 9+2^ 8......+2^ 1+2^ 0+2^ (-1)+2^ (-2)+2^ (-3)+......+2^ (-9)+2^ (-10) =[2^ 10-2^ (-10)*(1/2)]/（1-1/2) =2^ 11-2^ (-10) =2047又1023/1024