Solve the following:

​$$(1 + \frac{1}{x})(1 + \frac{1}{x + 1})(1 + \frac{1}{x + 2})(1 + \frac{1}{x + 3}) = ?$$​​

Correct option is D

To solve: 

​$$\left(1 + \frac{1}{x}\right) \left(1 + \frac{1}{x+1}\right) \left(1 + \frac{1}{x+2}\right) \left(1 + \frac{1}{x+3}\right) = ?$$​​

Solution:

​$$\begin{aligned}&\Rightarrow \left(1 + \frac{1}{x}\right) \left(1 + \frac{1}{x+1}\right) \left(1 + \frac{1}{x+2}\right) \left(1 + \frac{1}{x+3}\right) \\&\Rightarrow \left(\frac{(x+1)}{x}\right) \times \left(\frac{(x+1)+1}{(x+1)}\right) \times \left(\frac{(x+2)+1}{(x+2)}\right) \times \left(\frac{(x+3)+1}{(x+3)}\right) \\&\Rightarrow \left(\frac{(x+1)}{x}\right) \times \left(\frac{(x+2)}{(x+1)}\right) \times \left(\frac{(x+3)}{(x+2)}\right) \times \left(\frac{(x+4)}{(x+3)}\right) \\&\Rightarrow \frac{(x+2)}{x} \times \frac{(x+3)}{(x+2)} \times \frac{(x+4)}{(x+3)} \\&\Rightarrow \frac{(x+4)}{x}\end{aligned}$$​​

Hence, option (d) is the correct answer.