这道题用错位相减法.原式/2=1/4n+3/8n+...+(2n-1)/n*2^(n+1)所以原式/2=1/2n+2/4n+2/8n+...+2/n*2^n-(2n-1)/n*2^(n+1)n*原式/2=1/2+1-(1/2)^(n-1)-(2n-1)/2^(n+1)原式=3/n-(2n+7)/2^(n+1)