a=1*（1/2）+3*（1/4）+5*（1/8）+.+（2n-3)*1/2^(n-1)+(2n-1)*1/2^n
2a=1*1+3*（1/2）+5*（1/4）+.+（2n-1)*1/2^(n-1)
相减
2a-a=a=1+2*(1/2)+2*(1/4)+……+2*1/2^(n-1)-(2n-1)*1/2^n
2*(1/2)+2*(1/4)+……+2*1/2^(n-1)
=2*(1/2)*[1-(1/2)^(n-1)]/(1-1/2)
=2-1/2^(n-2)
所以原式=1+2-1/2^(n-2)-(2n-1)*1/2^n
=3-4*1/2^n-(2n-1)*1/2^n
=3-(2n+3)*1/2^n