an=a(n-1)+1/n(n-1)=a(n-1)+1/(n-1)-1/n
an+1/n=a(n-1)+1/(n-1)
a1+1=1+1=2
数列{an+1/n}是各项均等于2的常数数列.
an+1/n=2
an=2-1/n
a1=2-1=1,同样满足.
数列{an}的通项公式为an=2-1/n
a1=1
a2=2-1/2=3/2
a3=2-1/3=5/3
a4=2-1/4=7/4
a5=2-1/5=9/5