1/[a(a+1)]=1/a-1/(a+1)1/[(a+1)(a+2)]=1/(a+1)-1/(a+2)1/[(a+2)(a+3)]=1/(a+2)-1/(a+3)……1/[(a+2005)(a+2006)]=1/(a+2005)-1/(a+2006)1/[(a+2006)(a+2007)]=1/(a+2006)-1/(a+2007)原式1/[a(a+1)]+1/[(a+1)(a+2)]+...