24. The $n$th term in a certain sequence is calculated by multiplying together all the numbers $\sqrt{1+\frac{1}{k}}$, where $k$ takes all the integer values from 2 to $n+1$ inclusive. For example, the third term in the sequence is $\sqrt{1+\frac{1}{2}} \times \sqrt{1+\frac{1}{3}} \times \sqrt{1+\frac{1}{4}}$.
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