\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" alt=" \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" align="absmiddle" class="latex-formula">
т.к.
\infty } {( \frac{2}{3})}^{n} = 0" alt="\lim_{n - > \infty } {( \frac{2}{3})}^{n} = 0" align="absmiddle" class="latex-formula">