Producing an integer

Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?

Age

14 to 16

Challenge level

Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving

Being curious Being resourceful Being resilient Being collaborative

Problem

For which values of $n$ is the product $(1 + \frac{1}{2}) (1 + \frac{1}{3}) (1 + \frac{1}{4}) . . . (1 + \frac{1}{n})$ equal to an integer?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.