Question

Find the value of \(\left( {1 - \frac{1}{5}} \right)\left( {1 - \frac{1}{6}} \right)\left( {1 - \frac{1}{7}} \right)....\left( {1 - \frac{1}{{39}}} \right)\)
1. 4/39
2. 2/39
3. 5/39
4. 8/39

Answer 1

Correct Answer - Option 1 : 4/39

Given:

\(\left( {1 - \frac{1}{5}} \right)\left( {1 - \frac{1}{6}} \right)\left( {1 - \frac{1}{7}} \right)....\left( {1 - \frac{1}{{39}}} \right)\)

Concept used:

Simplification

Calculation:

⇒ \(\frac{4}{5} \times \frac{5}{6} \times \frac{6}{7} \times .....\frac{{38}}{{39}}\)

∴ Ans : 4/39