Question

1/15 + 1/35 + 1/63 + ..+ 1/129.15 =?

Answer 1

\(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+.....+\frac{1}{129.15}=\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+....+\frac{1}{1935}\)

=\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+.....+\frac{1}{43.45}\)

=\(\frac{1}{2}\left(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+.....+\frac{1}{43}-\frac{1}{45}\right)\)

=\(\frac{1}{2}\left(\frac{1}{2}-\frac{1}{45}\right)\)

=\(\frac{1}{2}.\frac{43}{90}\)

=\(\frac{43}{180}\)