Question

1/(x+2)(x+3) +1/(x+3)(x+4) +1/(x+4)(x+5)=?

Answer 1

1/(x+2)(x+3) +1/(x+3)(x+4) +1/(x+4)(x+5)

=1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+1/(x+4)-1/(x+5)

=1/(x+2)-1/(x+5)

=3/[(x+2)(x+5)]

1/（x+1）（x+2） +1/(x+2)(x+3) +1/(x+3)(x+4)+……+1/（x+100）（x+101）

=1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+……+1/（x+100)-1/(x+101)

=1/(x+2)-1/(x+101)

=(101-2)/(x+2)(x+101)

=99/[(x+2)(x+101)]