Tính giới hạn T = lim ( √ 16 ^(n + 1) + 4 ^n − √ 16 ^(n + 1) + 3 ^n )

Chọn C

Ta có \(T = \lim \left( {\sqrt {{{16}^{n + 1}} + {4^n}}  - \sqrt {{{16}^{n + 1}} + 3} } \right)\)\( = \lim \frac{{{4^n} - {3^n}}}{{\sqrt {{{16}^{n + 1}} + {4^n}}  + \sqrt {{{16}^{n + 1}} + {3^n}} }}\)

\( = \lim \frac{{{4^n} - {3^n}}}{{\sqrt {{{16.16}^n} + {4^n}}  + \sqrt {{{16.16}^n} + {3^n}} }}\)\( = \lim \frac{{1 - {{\left( {\frac{3}{4}} \right)}^n}}}{{\sqrt {16 + {{\left( {\frac{1}{4}} \right)}^n}}  + \sqrt {16 + {{\left( {\frac{3}{4}} \right)}^n}} }}\)\( = \frac{1}{{4 + 4}}\)\( = \frac{1}{8}\).