А) 19/37:

$19/37 = 0.513513...$

$0.513513... = 0 + \cfrac{1}{1/0.513513...} = 0 + \cfrac{1}{1.948717...}$

$1.948717... = 1 + \cfrac{1}{1/0.948717...} = 1 + \cfrac{1}{1.052631...}$

$1.052631... = 1 + \cfrac{1}{1/0.052631...} = 1 + \cfrac{1}{18.999...}$

Таким образом, $19/37 = [0; 1, 1, 19]$.

б) 49/30:

$49/30 = 1.633333...$

$1.633333... = 1 + \cfrac{1}{1/0.633333...} = 1 + \cfrac{1}{1.578947...}$

$1.578947... = 1 + \cfrac{1}{1/0.578947...} = 1 + \cfrac{1}{1.727272...}$

$1.727272... = 1 + \cfrac{1}{1/0.727272...} = 1 + \cfrac{1}{1.375}$

Таким образом, $49/30 = [1; 1, 1, 1, 2]$.

в) 81/71:

$81/71 = 1.140845...$

$1.140845... = 1 + \cfrac{1}{1/0.140845...} = 1 + \cfrac{1}{7.086957...}$

$7.086957... = 7 + \cfrac{1}{1/0.086957...} = 7 + \cfrac{1}{11.5}$

Таким образом, $81/71 = [1; 7, 11]$.