Question

a1=1,am+n=am+an+mn,求1/an+1/a2+1/a3+.+1/2012=

Answer 1

令m=1,an+1=an+n+1 求得an=n(n+1)/2

1/an=2/n(n+1)=2(1/n-1/n+1)

所以1/an+1/a2+1/a3+.+1/a2012=2(1-1/2+1/2-1/3+……+1/2012-1/2013)=4024/2013