Question

1/x(x+1)+1/(x+1)(x+2)+……+1/(x+999)(x+1000)=?

Answer 1

1/x(x+1)+1/(x+1)(x+2)+……+1/(x+999)(x+1000)

=1/x-1/(x+1)+1/(x+1)-1/(x+2)+.+1/(x+999)-1/(x+1000)

=1/x-1/(x+1000)

=1000/(x(x+1000))

公式:1/n(n+1)=1/n-1/(n+1)