Question

1/2*1/3+1/3*1/4+1/4*1/5+1/5*1/6+1/6*1/7+1/7*1/8

Answer 1

\(\dfrac{1}{2}\).\(\dfrac{1}{3}\)+\(\dfrac{1}{3}\).\(\dfrac{1}{4}\)+\(\dfrac{1}{4}\).\(\dfrac{1}{5}\)+\(\dfrac{1}{5}\).\(\dfrac{1}{6}\)+\(\dfrac{1}{6}\).\(\dfrac{1}{7}\)+\(\dfrac{1}{7}\).\(\dfrac{1}{8}\)

=\(\left(\dfrac{1}{2}-\dfrac{1}{3}\right)\)+\(\left(\dfrac{1}{3}-\dfrac{1}{4}\right)+\left(\dfrac{1}{4}-\dfrac{1}{5}\right)+\left(\dfrac{1}{5}-\dfrac{1}{6}\right)+\left(\dfrac{1}{6}-\dfrac{1}{7}\right)+\left(\dfrac{1}{7}-\dfrac{1}{8}\right)\)

=\(\dfrac{1}{2}-\dfrac{1}{8}\)

=\(\dfrac{3}{8}\)