Problem #PRU-79391

Problems Methods Mathematical induction Mathematical induction (other) Calculus Number sequences Number sequences (other)

14–15 4.0

Problem

At what value of $k$ is the quantity $A_{k} = (19^{k} + 66^{k}) / k!$ at its maximum? You are given a number $x$ that is greater than 1. Is the following inequality necessarily fulfilled $⌊ \sqrt{\sqrt{x}} ⌋ = ⌊ \sqrt{\sqrt{x}} ⌋$ ?

To see the solution register and get verified.