How do I expand this product

Question

How do I expand the following product:

\begin{equation} \prod_{j=i+1}^n (1-\frac{1}{j}) \end{equation}

Wolfram Alpha tells me the answer is $i/n$, which is the answer I was looking for, but I have no idea how to derive this by hand.

Answer 1

The product expands as $$\frac i{\color{red}{i+1}}\cdot\frac{\color{red}{i+1}}{i+2}\cdots\frac{n-2}{\color{blue}{n-1}}\frac{\color{blue}{n-1}}n$$ which telescopes down to $\frac in$ (numerator and denominator of adjacent fractions cancel).