Question

计算：1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+9)(x+10)

Answer 1

1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+9)(x+10)

=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+……+1/(x+9)-1/(x+10)

=1/x-1/(x+10)

=(x+10-x)/{x(x+10)}

= 10/{x(x+10)}