Wyznaczamy granice.

$\text{A.}\underset{n\to \infty }{\lim }\left(a_n+b_n\right)=\underset{n\to \infty }{\lim }{a}_n+\underset{n\to \infty }{\lim }{b}_n=-2+\left(+\infty \right)=+\infty$  

$\text{B.}\underset{n\to \infty }{\lim }\left(a_n-b_n\right)=\underset{n\to \infty }{\lim }{a}_n-\underset{n\to \infty }{\lim }{b}_n=-2-\left(+\infty \right)=-\infty$  

$\text{C.}\underset{n\to \infty }{\lim }\left(a_n\cdot b_n\right)=\underset{n\to \infty }{\lim }{a}_n\cdot \underset{n\to \infty }{\lim }{b}_n=-2\cdot \left(+\infty \right)=-\infty$  

$\text{D.}\underset{n\to \infty }{\lim }\frac{a_n}{b_n}=\frac{\underset{n\to \infty }{\lim }{a}_n}{\underset{n\to \infty }{\lim }{b}_n}=\frac{-2}{+\infty }=0$  

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Odpowiedź: D