\(\lim \frac{{{3^n} - {4^n} + 1}}{{{3^n} + {2^n}}}\) bằng
A. 0
B. \( + \infty \)
C. \(- \infty \)
D. \( - \frac{4}{3}\]
\(\lim \frac{{{3^n} - {4^n} + 1}}{{{3^n} + {2^n}}} = \lim \frac{{{{\left( {\frac{3}{4}} \right)}^n} - 1 + {{\left( {\frac{1}{4}} \right)}^n}}}{{{{\left( {\frac{3}{4}} \right)}^n} + {{\left( {\frac{1}{2}} \right)}^n}}} = - \infty \)
Vì \(\lim \left[ {{{\left( {\frac{3}{4}} \right)}^n} - 1 + {{\left( {\frac{1}{4}} \right)}^n}} \right] = - 1 < 0\) và \(\lim \left[ {{{\left( {\frac{3}{4}} \right)}^n} + {{\left( {\frac{1}{2}} \right)}^n}} \right] = 0\)
Chọn C.
-- Mod Toán 11