Question

已知数列{an}满足a1＝1,an=a1＋1/2a2＋1/3a3+…＋1/(n－1)an

Answer 1

an=a1+(1/2)a2+(1/3)a3+...+[1/(n-2)]a(n-2)+[1/(n-1)]a(n-1)

a(n-1)=a1+(1/2)a2+(1/3)a3+...+[1/(n-2)]a(n-2)

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

an/n=a(n-1)/(n-1)

a1/1=1/1=1

数列{an/n}是各项都为1的常数数列

an/n=1

an=n

n=1时,a1=1,同样满足.

数列{an}的通项公式为an=n.