Question

计算2005/6+2005/12+2005/20+2005/30+...+2005/(2003×2004)+1/2004

Answer 1

原式=2005*(1/(2*3)+1/(3*4)+...+1/(2003*2004))+1/2004

=2005*(1/2-1/3+1/3-1/4+...+1/2003-1/2004)+1/2004

=2005*(1/2-1/2004)+1/2004

=2005/2-1

=2003/2