\(\lim\dfrac{3.4^n-2.13^n}{5^n+6.13^n}=\lim\dfrac{3.\left(\dfrac{4}{13}\right)^n-2}{\left(\dfrac{5}{13}\right)^n+6}=\dfrac{3.0-2}{0+6}=-\dfrac{1}{3}\)
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