MathDB

5

Part of 1983 Brazil National Olympiad

Problems(1)

smallest k such that 1 \le n ^{1/n} \le k for all positive integers n

Source: Brazilian Mathematical Olympiad 1983 P5

7/27/2018
Show that 1≤n1/n≤21 \le n^{1/n} \le 2 for all positive integers nn. Find the smallest kk such that 1≤n1/n≤k1 \le n ^{1/n} \le k for all positive integers nn.
number theoryminimumpositive integersInequality