Question

The simplified value of \(\left(1 - \dfrac{1}{3}\right) \left(1 - \dfrac{1}{4}\right) \left(1 - \dfrac{1}{5}\right).... \left(1 - \dfrac{1}{99}\right) \left(1 - \dfrac{1}{100}\right)\) is -
1. \(\dfrac{2}{99}\)
2. \(\dfrac{1}{25}\)
3. \(\dfrac{1}{50}\)
4. \(\dfrac{1}{100}\)

Answer 1

Correct Answer - Option 3 : \(\dfrac{1}{50}\)

Calculation:

\(\left(1 - \dfrac{1}{3}\right) \left(1 - \dfrac{1}{4}\right) \left(1 - \dfrac{1}{5}\right).... \left(1 - \dfrac{1}{99}\right) \left(1 - \dfrac{1}{100}\right)\)

⇒ \(\left(\dfrac{3-1}{3}\right) \left(\dfrac{4-1}{5}\right) \left(\dfrac{5-1}{5}\right).... \left(\dfrac{99-1}{99}\right) \left(\dfrac{100-1}{100}\right)\)

⇒ \(\left(\dfrac{2}{3}\right) \left(\dfrac{3}{4}\right) \left(\dfrac{4}{5}\right).... \left(\dfrac{98}{99}\right) \left(\dfrac{99}{100}\right)\)

⇒ \(\left(\dfrac{2}{100}\right)\)

⇒ \(\left(\dfrac{1}{50}\right)\)