Question

1/(1x2x3)+1/(2x3x4)+1/(3x4x5)+.1/(20x21x22)=?

Answer 1

1/(1*2*3)+1/(2*3*4)+1/(3*4*5)+.1/(20*21*22)

=1/2[1/1*2-1/2*3]+1/2[1/2*3-1/3*4]+1/2[1/3*4-1/4*5]+...+1/2[1/20*21-1/21*22]

=1/2[1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+...+1/20*21-1/21*22]

=1/2[1/2-1/21*22]

=1/2*115/231

=115/462