In Exercises $35-62,$ use the appropriate limit laws and theorems to determine the limit of the sequence or show that it diverges. $$ a_{n}=\frac{3-4^{n}}{2+7 \cdot 3^{n}} $$
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Step 1:** Apply the limit laws to simplify the expression: $$\lim_{n \to \infty} \frac{3-4^{n}}{2+7 \cdot 3^{n}}$$ $$= \lim_{n \to \infty} \frac{3}{2} \cdot \frac{1-4^{n}}{1+7 \cdot 3^{n}}$$ $$= \frac{3}{2} \cdot \lim_{n \to \infty} \frac{1-4^{n}}{1+7 \cdot Show more…
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