Question

Let x ∈ R such that

(2021 −2020/n)≤ x ≤( 2021 +2020/n)

for all positive integer n ≥ 10. Prove that x = 2021.

Answer 1

$\lim_{n->\infin}(2021-\frac{2020}n{})\le x\le\lim_{n->\infin}(2021+\frac{2020}{n})$

$2021\le x\le 2021$

$x=2021$