数列求和习题：Sn＝1/2+3/4+5/8+……+2n-1/2的n次方 求Sn
问题描述：
数列求和习题：Sn＝1/2+3/4+5/8+……+2n-1/2的n次方 求Sn
答
解析：∵Sn＝1/2+3/4+5/8+……+（2n-1）/2^n
2 Sn＝1+3/2+5/4+7/8+……+(2n-1)/2^(n-1)
∴Sn=1+2/2+2/4+2/8+……+2/2^(n-1)-(2n-1)/2^n
=1+1+1/2+1/4+1/8+……+1/2^(n-2)-(2n-1)/2^n
=1+[1-(1/2)^(n-1)]/(1-1/2)-(2n-1)/2^n
=1+2-1/2^(n-2))-(2n-1)/2^n
=3-(2n+3)/2^n