a(n+1)=an +1/[n(n+1)]=an +1/n -1/(n+1) a(n+1) +1/(n+1)=an +1/n a1 +1/1=1+1=2 数列{an +1/n}是各项均为2的常数数列. an +1/n=2 an=2-1/n=(2n-1)/n a2013=(2×2013-1)/2013=4025/2013
