Question

Suppose x is a positive real number such that {x}, [x] and x are in a geometric progression. Find the least positive integer n such that xⁿ > 100 . (Here [x] denotes the integer part of x and {x} = x – [x])

Answer 1

∵ {x}, [x], x are in GP let these be a, ar, ar²

Also as {x} = x – [x]

∴ a = ar² – ar

∵ a = {x} which lies in [0,1)