Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\dpi{110}\frac{2^{n+4}-2^{n+3}+2^{n+2}-2^{n+1}}{2^{n+4}}$ is gelijk aan	A.
	B.
	C.
	D. ${\color{DarkBlue} \frac{1}{2^{n+3}}}$
	E. ${\color{DarkBlue} \frac{1}{2^{n+2}}}$

[ 2-8675 - op net sinds 5.5.2021-(E)-17.1.2025 ]

Translation in E N G L I S H

$\frac{2^{n+4}-2^{n+3}+2^{n+2}-2^{n+1}}{2^{n+4}}$ is equal to	A.
	B.
	C.
	D. ${\color{DarkBlue} \frac{1}{2^{n+3}}}$
	E. ${\color{DarkBlue} \frac{1}{2^{n+2}}}$

Oplossing - Solution

$\frac{2^{n+4}-2^{n+3}+2^{n+2}-2^{n+1}}{2^{n+4}}=1-\frac{1}{2}+\frac{1}{2^2}-\frac{1}{2^3}=1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}=\frac{8-4+2-1}{8}=\frac{5}{8}$