Problem: The value of 12−12−12−12\dfrac{1}{2-\dfrac{1}{2-\dfrac{1}{2-\dfrac{1}{2}}}}2−2−2−21111 is
Answer Choices:
A. 3/43 / 43/4
B. 4/54 / 54/5
C. 5/65 / 65/6
D. 6/76 / 76/7
E. 6/56 / 56/5 Solution:
12−12−12−12=12−12−23=12−34=45\dfrac{1}{2-\dfrac{1}{2-\dfrac{1}{2-\dfrac{1}{2}}}}=\dfrac{1}{2-\dfrac{1}{2-\dfrac{2}{3}}}=\dfrac{1}{2-\dfrac{3}{4}}=\dfrac{4}{5}2−2−2−21111=2−2−3211=2−431=54.