Question

2分之1+6分之1＋12分之1＋20分之1……＋4022030分之1的值

Answer 1

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