求和2x1/2+4x1/4+6x1/8+8x1/16+…+2nx1/2^n要详解答案,急用!
问题描述：
求和2x1/2+4x1/4+6x1/8+8x1/16+…+2nx1/2^n要详解答案,急用!
答
设Sn=原式,2Sn=2+4x1/2+6x1/4+……+2nx1/2^(n-1)
Sn= 2x1/2+4x1/4+……+2(n-1)/2^(n-1)+2nx1/2^n
Sn=2Sn-Sn=2+2[1/2+1/4+……+1/2^(n-1)]-2nx1/2^n=4-(n+2)/2^(n-1)