$\left(1 - \dfrac{1}{2}\right)\left(1 - \dfrac{1}{3}\right)\left(1 - \dfrac{1}{4}\right)\left(1 -…

$\left(1 - \dfrac{1}{2}\right)\left(1 - \dfrac{1}{3}\right)\left(1 - \dfrac{1}{4}\right)\left(1 - \dfrac{1}{5}\right)$ equals
  1. $\dfrac{1}{5}$
  2. $\dfrac{1}{2}$
  3. $\dfrac{1}{120}$
  4. $0$

Solution

Telescoping: $\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot\dfrac{4}{5} = \dfrac{1}{5}$.

Asked in: IMO

Practice more RATIONAL NUMBERS questions on Aicharya