Question

A1=1 An=A1+1/2×A2+1/3×A3+.1/(n-1)×(An-1)(n≥2),An=?

Answer 1

设Bn=An/n,Bn的前n项和为Tn,An=T(n-1),Bn=T(n-1)/n,Tn-T(n-1)=Bn=T(n-1)/n 即Tn/(n+1)=T(n-1)/n=(T1)/2=(B1)/2=1/2 即 An=Tn-1=n/2(n≥2),A1=1