Question

Write the following expression as a fraction in lowest terms:
\[2 + \cfrac{2}{2 + \cfrac{3}{3 + \cfrac{4}{4 + 5}}}.\]

Answer 1

Step-by-step explanation:

$\[2 + \cfrac{2}{2 + \cfrac{3}{3 + \cfrac{4}{4 + 5}}}\]=$

$\[2 + \cfrac{2}{2 + \cfrac{3}{3 + \cfrac{4}{9}}}\]=$

$\[2 + \cfrac{2}{2 + \cfrac{3}{\cfrac{31}{9}}}\]=$

$\[2 + \cfrac{2}{2 + \cfrac{27}{31} }}}\]=$

$\[2 + \cfrac{2}{ \cfrac{62+27}{31} }}}\]=$

$\[2 + \cfrac{2}{ \cfrac{89}{31} }}}\]=$

$\[2 + \cfrac{62}{{89} }}}\]=$

$\[2 \cfrac{62}{{89} }}}\]$