数列an满足a1=1,且对任意m,n都有am+n=am+an+mn,则1/a1+1/a2+...+1/a2010=
问题描述：
数列an满足a1=1,且对任意m,n都有am+n=am+an+mn,则1/a1+1/a2+...+1/a2010=
答
令m=1有a(n+1)=a(n)+a(1)+n=a(n)+n+1a(n)=a(n-1)+na(n-1)=a(n-2)+n-1...a(2)=a(1)+2那么把式子左右分别相加,得到a(n)=a(1)+2+...+n=(n+1)n/21/a(1)+1/a(2)+...+1/a(2010)=2/(1*2)+2/(2*3)+...+2/(2010*2011)=2[1/(1*...