Question

Вычислите предел пожалуйста

Answer 1

$lim_{n - > infty } frac{ {2}^{n + 1} + {3}^{n + 1} }{ {2}^{n} + {3}^{n} } = \ = lim_{n - > infty } frac{ 2 times {2}^{n} + 3 times {3}^{n} }{ {2}^{n} + {3}^{n} } = \ = lim_{n - > infty } frac{ {3}^{n} (2 times ( frac{2}{3})^{n} + 3)}{ {3}^{n}( {( frac{2}{3}) }^{n} + 1)} = \ = lim_{n - > infty } frac{ 2 times ( frac{2}{3})^{n} + 3}{{( frac{2}{3}) }^{n} + 1} = \ = frac{2 times 0 + 3}{0 + 1} = 3$
т.к.
$lim_{n - > infty } {( frac{2}{3})}^{n} = 0$