1/2+1/6+1/12+1/20+.+1/4022030
=1/1*2 + 1/2*3 + 1/3*4 + 1/4*5 + ...+ 1/2005*2006
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/2005-1/2006
=1-1/2006
=2005/2006
1/2+1/6+1/12+1/20+.+1/4022030=?
1/2+1/6+1/12+1/20+.+1/4022030
=1/1*2 + 1/2*3 + 1/3*4 + 1/4*5 + ...+ 1/2005*2006
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/2005-1/2006
=1-1/2006
=2005/2006