# Find the value of given expression. $\left( {1 + \;\frac{1}{P}} \right)\left( {1 + \;\frac{1}{{P + 1}}} \right)\left( {1 + \;\frac{1}{{P + 2}}} \righ 0 votes 26 views in Aptitude closed Find the value of given expression. \(\left( {1 + \;\frac{1}{P}} \right)\left( {1 + \;\frac{1}{{P + 1}}} \right)\left( {1 + \;\frac{1}{{P + 2}}} \right)\left( {1 + \;\frac{1}{{P + 3}}} \right)\left( {1 + \;\frac{1}{{P + 4}}} \right)\left( {1 + \;\frac{1}{{P + 5}}} \right) + \frac{{P - 6}}{P} + \;\frac{{19}}{{P + 18}} + \;\frac{{19}}{{P - 18}}\;$

1. $\frac{{12}}{P} + \frac{{38P}}{{P.P - 324}}$
2. $\frac{{12}}{P} + \frac{{19}}{{P.P - 324}}$
3. $2 + \frac{{38P}}{{P.P - 324}}$
4. $12 + \frac{{38P}}{{P.P - 324}}$

by (25.6k points)
selected by

Correct Answer - Option 3 : $2 + \frac{{38P}}{{P.P - 324}}$

Calculation:

$\left( {1 + \;\frac{1}{P}} \right)\left( {1 + \;\frac{1}{{P + 1}}} \right)\left( {1 + \;\frac{1}{{P + 2}}} \right)\left( {1 + \;\frac{1}{{P + 3}}} \right)\left( {1 + \;\frac{1}{{P + 4}}} \right)\left( {1 + \;\frac{1}{{P + 5}}} \right) + \frac{{P - 6}}{P} + \;\frac{{19}}{{P + 18}} + \;\frac{{19}}{{P - 18}}\;$

$\Rightarrow \left( {\frac{{P + 1}}{P}} \right)\left( {\frac{{P + 2}}{{P + 1}}} \right)\left( {\frac{{P + 3}}{{P + 2}}} \right)\left( {\frac{{P + \;4}}{{P + 3}}} \right)\left( {\frac{{P + 5}}{{P + 4}}} \right)\left( {\frac{{P + \;6}}{{P + 5}}} \right) + \frac{{P - 6}}{P} + \frac{{19\left( {P - 18 + P + 18} \right)}}{{P.P - 18 \times 18}}$

$\Rightarrow \left( {\frac{{P + \;6}}{P}} \right) + \frac{{P - 6}}{P} + \;\frac{{38P}}{{P.P - 324}}$

$\Rightarrow \frac{{2P}}{P} + \frac{{38P}}{{P.P - 324}}$

$\Rightarrow 2 + \frac{{38P}}{{P.P - 324}}$