MathNet 2004 — Part 02 Question 44

Question 44

For which natural numbers $n$ the product
$$
\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right) \cdots\left(1+\frac{1}{n}\right)
$$
is it an integer?

For odd $n$
for no $n$.
for $n$ even
for $n$ multiple of 3
for each $n$