/sci/ - Science & Math

>>15128947
Everything is positive.
If [math]b_n[/math] is bounded above, [math]\displaystyle \lim_{n \to \infty} a_n - b_n = \infty[/math] implies [math]\displaystyle \lim_{n \to \infty} \dfrac{a_n}{b_n} = \infty[/math].
If [math]b_n[/math] is bounded below, [math]\displaystyle \lim_{n \to \infty} \dfrac{a_n}{b_n} = \infty[/math] implies [math]\displaystyle \lim_{n \to \infty} a_n - b_n = \infty[/math]