Alanonala

Here is a very interesting continued fraction expansion for pi/2 :

$\pi /2=1+{\cfrac {1}{1+{\cfrac {1}{1/2+{\cfrac {1}{1/3+{\cfrac {1}{1/4+{\cfrac {1}{1/5+{\cfrac {1}{1/6+{\cfrac {1}{1/7+{\cfrac {1}{1/8+{\cfrac {1}{1/9+{\cfrac {1}{1/10+{\cfrac {1}{1/11+{\cfrac {1}{1/12+{\cfrac {1}{1/13+{\cfrac {1}{1/14+{\cfrac {1}{1/15+\ddots }}}}}}}}}}}}}}}}}}}}}}}}}}}}}}$