MathDB
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} <spanclass=latexbold>(E)</span> x>2 but finite <span class='latex-bold'>(E)</span>\ x > 2 \text{ but finite}