数列求和:1/2+3/4+5/8+7/16+.+(2n-1)/(2^n)
问题描述:
数列求和:1/2+3/4+5/8+7/16+.+(2n-1)/(2^n)
答
-2*(1/2)^(n+1)-4*(1/2)^(n+1)*(n+1)+3
答
设原式=Sn2*Sn=1+3/2+5/4+7/8+...+(2n-1)/(2^(n-1))上式减去原式(错位相减)得出Sn=1+2*1/2+2*1/4+2*1/8+...+2*1/(2^(n-1))-(2n-1)/(2^n) =1-(2n-1)/(2^n)+[1+1/2+1/4+...+1/(2^(n-2))] =1-(2n-1)/(2^n)+2-1/(2^(...