Question

高二数列问题Sn=1/2+3/4+5/8+…+(2n-3)/2^(n-1)+(2n-1)/2^n求Sn的表达式~请给位尽

Answer 1

an=(2n-1)/2^n

sn= 1/2+3/4+5/8+7/16+...+(2n-3)/2^n-1 +(2n-1)/2^n

2sn=1+3/2+5/4+7/8+9/16+...+(2n-1)/2^n-1

sn=2sn-sn=1+2(1/2+1/4+1/8+...+1/2^n-1)-(2n-1)/2^n

=1+2*(1/2-1/2^n)/(1-1/2)-(2n-1)/2^n

=1+2-4/2^n -(2n-1)/2^n

=3-(3+2n)/2^n