, 2017

The $n$th term in a certain sequence is calculated by multiplying together all the numbers $\sqrt{1 + \dfrac{1}{k}}$, where $k$ takes all the integer values from $2$ to $n+1$ inclusive. For example, the third term in the sequence is $\sqrt{1+\dfrac{1}{2}} \times \sqrt{1+\dfrac{1}{3}} \times \sqrt{1+\dfrac{1}{4}}$. Which is the smallest value of $n$ for which the $n$th term of the sequence is an integer?

(A) $3$ (B) $5$ (C) $6$ (D) $7$ (E) more than $7$