# True or false: if a n </msub> is any decreasing sequence of positive real number

True or false: if ${a}_{n}$ is any decreasing sequence of positive real numbers and ${b}_{n}$ is any sequence of real numbers converges to $0$, then $\frac{{a}_{n}}{{b}_{n}}$ diverges.
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Maeve Holloway
if ${a}_{n}={e}^{-n}$ and ${b}_{n}=\frac{1}{{n}^{2}}$ then
$\left({a}_{n}\right)$ is a decreasing sequence of positive numbers and $\underset{+\mathrm{\infty }}{lim}{b}_{n}=0$
but
$\frac{{a}_{n}}{{b}_{n}}={n}^{2}{e}^{-n}\to 0.$
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Jaeden Weaver
Hint: Take ${a}_{n}={b}_{n}=\frac{1}{n}$