Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\displaystyle \lim_{n \to +\infty} \sqrt[n]{\frac{1}{2^n+4^n}$	A. 1
B.
C.
D.
E.

$\lim_{n\rightarrow +\infty}\sqrt[n]{\frac{1}{2^n+4^n}} \newline =\lim_{n\rightarrow +\infty}\sqrt[n]{4^n\left (\frac{2^n}{4^n+1} \right )}\newline =\lim_{n\rightarrow +\infty}\frac{1}{4\cdot \sqrt[n]{0,5^n+1}}\newline =\frac{1}{4}\lim_{n\rightarrow +\infty}\frac{1}{\sqrt[n]{0,5^n+1}}\newline =\frac{1}{4}\cdot \lim_{n\rightarrow +\infty}\frac{1}{\sqrt[n]{1}}=\frac{1}{4}\cdot \frac{1}{1}=\frac{1}{4}$