Question

Prove that the set A given by A:={2020/n +n² : n∈N} is unbounded above.

Answer 1

A function is bounded above if there is a real number, k, such that for all of x, f(x) ≤ k.

The number k is called the upper bound.

because A=2020/n+n², and

if $\lim _{n \rightarrow \infty} n^{2}+\frac{2020}{n}$ =infinity, it means k equals to infinity and A is unbounded above.

$\lim _{n \rightarrow \infty} n^{2}+\frac{2020}{n}$ = $\lim _{n \rightarrow \infty}$ ($\infty$)²+0=$\infty$, so the set A is unbounded above