Question

已知数列an满足a1=1/2 a1+a2+a3+……+an=n^2+an 求an sn

Answer 1

s(n)=n^2a(n)

a(n+1)=s(n+1)-s(n)=(n+1)^2a(n+1)-n^2a(n)

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

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

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

(n+2)(n+1)a(n+1)=(n+1)na(n)=...=(1+1)*1*a(1)=1

a(n)=1/[n(n+1)] = 1/n - 1/(n+1)