\[b_{0}+\cfrac{a_{1}}{b_{1}+\cfrac{a_{2}}{b_{2}+\cfrac{a_{3}}{b_{3}+\cdots}}}={b%
_{0}+\cfrac{a_{1}/b_{1}}{1+\cfrac{a_{2}/(b_{1}b_{2})}{1+\cfrac{a_{3}/(b_{2}b_{%
3})}{1+\cdots\cfrac{a_{n}/(b_{n-1}b_{n})}{1+\cdots}}}}}={b_{0}+\cfrac{1}{(%
\ifrac{1}{a_{1}})b_{1}+\cfrac{1}{(\ifrac{a_{1}}{a_{2}})b_{2}+\cfrac{1}{(\ifrac%
{a_{2}}{(a_{1}a_{3})})b_{3}+\cfrac{1}{(\ifrac{a_{1}a_{3}}{(a_{2}a_{4})})b_{4}+%
\cdots}}}}}.\]