Telescoping product
= Telescoping product
{title2=$\prod_{i=m}^{n}b_{i+1}/b_i=b_{n+1}/b_m$}
A product in which numerator and denominator factors cancel between successive terms. For nonzero $b_m,\ldots,b_{n+1}$,
$$
\prod_{i=m}^{n}\frac{b_{i+1}}{b_i}=\frac{b_{n+1}}{b_m}.
$$
One can prove the identity directly by cancellation or by <mathematical induction> on $n$. Factoring a more complicated product into two such ratios often reveals an otherwise hidden closed expression.