已知在数列{an}中,a1=2,na[n+1]=(n+1)an+2 (n∈N*),a10=( ) 注：[ ]为下标

Question

已知在数列{an}中,a1=2,na[n+1]=(n+1)an+2 (n∈N*),a10=( ) 注：[ ]为下标

Answer 1

两边除以n(n+1)
a(n+1)/(n+1)=an/n+2/n(n+1)
a(n+1)/(n+1)-an/n=2/n(n+1)=2[1/n-1/(n+1)]
a10/10-a9/9=2(1/10-1/11)
a9/9-a8/8=2(1/9-1/10)
……
a2/2-a1/1=2(1/2-1/3)
相加
a10/10-a1/1=2*(1/2-1/11)=9/11
a10=310/11