Wiskunde Multiple Choice Vraag

$\inline\\1+\frac1a+\frac1{a^2}+\frac1{a^3}+\cdots=10\\\\1+\frac1b+\frac1{b^2}+\frac1{b^3}+\cdots=2\\$ Dan is \(\large\frac ab=\)	A. \(\large\frac{1}{5}\)
B. \(\large\frac{5}{9}\)
C. \(\sqrt5\)
D. \(\large\frac{9}{5}\)
E. \(5\)

$\inline\\1+\frac1a+\frac1{a^2}+\frac1{a^3}+\cdots=10\;\Leftrightarrow\:\frac{1}{1-\frac1a}=10\;\Leftrightarrow\:\frac{a}{a-1}=10\;\Leftrightarrow\:a=10a-10\;\Leftrightarrow\:9a=10\\\\1+\frac1b+\frac1{b^2}+\frac1{b^3}+\cdots=2\;\Leftrightarrow\:\frac{1}{1-\frac1b}=2\;\Leftrightarrow\:\frac{b}{b-1}=2\;\Leftrightarrow\:b=2b-2\;\Leftrightarrow\:b=2\\$

$\huge\frac ab=\frac{9a}{9b}=\frac{10}{18}=\frac59$