Question

设数列{An}和{bn}满足A1=1/2,2nA(n+1)=(n+1)An,且Bn=ln(1+An)+1/2(An)2,

Answer 1

2na(n+1)=(n+1)a(n),

2^(n+1)*n*a(n+1)=(n+1)*2^n*a(n),

2^(n+1)*a(n+1)/(n+1)=2^n*a(n)/n=...=2^1*a(1)/1=2*(1/2)=1,

a(n)=n*2^(-n),n=1,2,...

b(n)=ln[1+a(n)]+(1/2)[a(n)]^2=ln[1+n*2^(-n)]+(1/2)[n2^(-n)]^2,..

b(n)表达式有误吧.