Question

1/1.2 + 1/2.3 + 1/3.4 + ... + 1/2003.2004 = ?

Answer 1

\(\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{2003\times2004}=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2003}-\frac{1}{2004}=1-\frac{1}{2004}=\frac{2003}{2004}\)

Answer 2

1/1.2+1/2.3+1/4.4+...1/2003.2004

=1-1/2004

=2003/2004