等号两边同除以n(n+1)(n+2)
a(n+1)/(n+1)(n+2)=an/n(n+1)+2
a1/(1*2)=3/2
所以{a(n)/n(n+1)}是以3/2为首项,2为公差的等差数列
a(n)/n(n+1)=3/2+2(n-1)=2n-1/2
a(n)=(2n-1/2)n(n+1)