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Suppose that $\{a_n\}_{n=1}^\infty$ and $\{b_n\}_{n=1}^\infty$ are sequences and $\lim_{n\to\infty} a_n=1\;,\quad\lim_{n\to\infty} b_n=0\;.$

Which of the following sequences does NOT converge?

A

$\{a_n+b_n\}_{n=1}^\infty$

B

$\{a_n-b_n\}_{n=1}^\infty$

C

$\{a_nb_n\}_{n=1}^\infty$

D

$\left\{\frac{a_n}{b_n}\right\}_{n=1}^\infty$

E

$\left\{\frac{b_n}{a_n}\right\}_{n=1}^\infty$

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