MathDB

real members

Source: Austria 1989

July 10, 2009

inductionalgebrapolynomialalgebra proposed

Problem Statement

Consider the set

S_n

of all the

2^n

numbers of the type

2\pm \sqrt{2 \pm \sqrt {2 \pm ...}},

where number

2

appears n\plus{}1 times.

(a)

Show that all members of

S_n

are real.

(b)

Find the product

P_n

of the elements of

S_n

.

Back to Problems View on AoPS