The value of $$\left[ {1 + \frac{1}{{x + 1}}} \right]$$ $$\left[ {1 + \frac{1}{{x + 2}}} \right]$$ $$\left[ {1 + \frac{1}{{x + 3}}} \right]$$ $$\left[ {1 + \frac{1}{{x + 4}}} \right]$$   $${\text{is}} = ?$$

$$\left[ {1 + \frac{1}{{x + 1}}} \right]$$ $$\left[ {1 + \frac{1}{{x + 2}}} \right]$$ $$\,\left[ {1 + \frac{1}{{x + 3}}} \right]$$ $$\left[ {1 + \frac{1}{{x + 4}}} \right]$$
$$ = \left[ {\frac{{\left( {x + 1} \right) + 1}}{{x + 1}}} \right]$$  $$\left[ {\frac{{\left( {x + 2} \right) + 1}}{{x + 2}}} \right]$$ $$\left[ {\frac{{\left( {x + 3} \right) + 1}}{{x + 3}}} \right]$$ $$\left[ {\frac{{\left( {x + 4} \right) + 1}}{{x + 4}}} \right]$$
$$\eqalign{ & = \left( {\frac{{x + 2}}{{x + 1}}} \right)\left( {\frac{{x + 3}}{{x + 2}}} \right)\left( {\frac{{x + 4}}{{x + 3}}} \right)\left( {\frac{{x + 5}}{{x + 4}}} \right) \cr & = \frac{{x + 5}}{{x + 1}} \cr} $$