h_xiaochun
幼苗
共回答了20个问题采纳率:90% 举报
s(n)=a(1)+a(2)+...+a(n-1)+a(n)=(3*1-1)*1 + (3*2-1)*2 + ...+ [3(n-1)-1]*2^(n-2) + (3n-1)*2^(n-1)
2s(n)=(3*1-1)*2 + (3*2-1)*2^2 + ...+ [3(n-1)-1]*2^(n-1) + (3n-1)*2^n,
s(n)=2s(n)-s(n)=-(3*1-1)*1 - 3[2 + 2^2 + ...+ 2^(n-1)] + (3n-1)*2^n
=-3[1+2+2^2+...+2^(n-1)] + 1 +(3n-1)*2^n
= 1 + (3n-1)*2^n - 3[2^n-1]/(2-1)
= 1 + (3n-1)*2^n - 3*2^n + 3
= 4 + (3n-4)*2^n
1年前
4