Tính giới hạn lim 3^n − 4^n + 5^n/3^n + 4^n − 5^n .

\(\lim \frac{{{3^n} - {4^n} + {5^n}}}{{{3^n} + {4^n} - {5^n}}}\)\( = \lim \frac{{\frac{{{3^n}}}{{{5^n}}} - \frac{{{4^n}}}{{{5^n}}} + 1}}{{\frac{{{3^n}}}{{{5^n}}} + \frac{{{4^n}}}{{{5^n}}} - 1}}\)\( = \lim \frac{{{{\left( {\frac{3}{5}} \right)}^n} - {{\left( {\frac{4}{5}} \right)}^n} + 1}}{{{{\left( {\frac{3}{5}} \right)}^n} + {{\left( {\frac{4}{5}} \right)}^n} - 1}}\)\( = - 1\).