1/2+1/2+3/8+……+n/(2^n)等于?求破解此类型题之道.顺便写下过程.

Question

1/2 +1/2+3/8 +……+n/(2^n) 等于?求破解此类型题之道.顺便写下过程.

Answer 1

{an}等差数列,公差为d,{bn}等比数列,公比为q(q≠1)Sn=a1/b1+a2/b2+……+an/bnqSn= a1/b2+……+a(n-1)/bn+an/b(n+1)Sn-qSn=a1/b1+d/b2+d/b3+……d/bn-an/b(n+1)Sn=1/2 +2/4+3/8 +……+n/(2^n) (1/2)Sn= 1/4 +2/8 +…...