Find the value of\[\cfrac{1}{1 + \cfrac{1}{4 + \cfrac{1}{4 + \cfrac{1}{4 + \cfrac{1}{4}}}}}.\]
4 + 1/4 = 17/4
4 + 4/17 = 72/17
4 + 17/72 = 305/72
1 + 72 / 305 = 377/305
1/ [ 377/305] = 305 / 377
