Telescoping product (${\prod }_{i=m}^n{b}_{i+1}/b_i=b_{n+1}/b_m$)

A product in which numerator and denominator factors cancel between successive terms. For nonzero $b_m,\dots ,b_{n+1}$,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.