Question

1/1*2+1/2*3+1/3*4+1/4*5+.+1/1000*1001

Answer 1

1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+……+1/(1000×10001)

=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/1000-1/1001)

=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/1000-1/1001

=1-1/1001

=1000/1001