Question

2/(x+1)(x+3)+2/(x+3)(x+5)+·····+2/(x+2007)(x+2009)

Answer 1

2/(x+1)(x+3)+2/(x+3)(x+5)+·····+2/(x+2007)(x+2009)

=1/(x+1)-1/(x+3)+1/(x+3)-1/(x+5)+·····+1/(x+2007)-1/(x+2009)

=1/(x+1)-1/(x+2009)

=2008/(x+1)(x+2009)

=2008/(x²+2010x+2009)