Infinite Nested Radical
Source:
February 1, 2009
Problem Statement
If x \equal{} \sqrt {1 \plus{} \sqrt {1 \plus{} \sqrt {1 \plus{} \sqrt {1 \plus{} \cdots}}}}, then:
(A)\ x \equal{} 1 \qquad(B)\ 0 < x < 1 \qquad(C)\ 1 < x < 2 \qquad(D)\ x\text{ is infinite}