Tính giới hạn \(\lim\dfrac{3^n-2\cdot5^{n+1}}{2^{n+1}+5^n}\).
\(-15\) | |
\(-10\) | |
\(10\) | |
\(15\) |
Chọn phương án B.
Dùng máy tính cầm tay:
Chọn phương án B.
\(\begin{aligned}
\lim\dfrac{3^n-2\cdot5^{n+1}}{2^{n+1}+5^n}&=\lim\dfrac{3^n-2\cdot5^n\cdot5}{2^n\cdot2+5^n}\\
&=\lim\dfrac{3^n-10\cdot5^n}{2\cdot2^n+5^n}\\
&=\lim\dfrac{\dfrac{3^n}{5^n}-10}{2\cdot\dfrac{2^n}{5^n}+1}\\
&=\lim\dfrac{\left(\dfrac{3}{5}\right)^n-10}{2\cdot\left(\dfrac{2}{5}\right)^n+1}\\
&=\dfrac{0-10}{2\cdot0+1}=-10.
\end{aligned}\)