Question

1/2+1/6+1/12+1/20+.+1/380+1/420 等于?

Answer 1

1/2+1/6+1/12+1/20+.+1/380+1/420

=1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+.+1/(19×20)+1/(20×21)

=1-1/2+1/2-1/3+1/3-1/4+...+1/20-1/21

=1-1/21

=20/21