Correct Answer - Option 3 :
\(2 + \frac{{38P}}{{P.P - 324}}\)
Calculation:
\(\left( {1 + \;\frac{1}{P}} \right)\left( {1 + \;\frac{1}{{P + 1}}} \right)\left( {1 + \;\frac{1}{{P + 2}}} \right)\left( {1 + \;\frac{1}{{P + 3}}} \right)\left( {1 + \;\frac{1}{{P + 4}}} \right)\left( {1 + \;\frac{1}{{P + 5}}} \right) + \frac{{P - 6}}{P} + \;\frac{{19}}{{P + 18}} + \;\frac{{19}}{{P - 18}}\;\)
\(\Rightarrow \left( {\frac{{P + 1}}{P}} \right)\left( {\frac{{P + 2}}{{P + 1}}} \right)\left( {\frac{{P + 3}}{{P + 2}}} \right)\left( {\frac{{P + \;4}}{{P + 3}}} \right)\left( {\frac{{P + 5}}{{P + 4}}} \right)\left( {\frac{{P + \;6}}{{P + 5}}} \right) + \frac{{P - 6}}{P} + \frac{{19\left( {P - 18 + P + 18} \right)}}{{P.P - 18 \times 18}}\)
\( \Rightarrow \left( {\frac{{P + \;6}}{P}} \right) + \frac{{P - 6}}{P} + \;\frac{{38P}}{{P.P - 324}}\)
\(\Rightarrow \frac{{2P}}{P} + \frac{{38P}}{{P.P - 324}}\)
\(\Rightarrow 2 + \frac{{38P}}{{P.P - 324}}\)