Comparing 2 infinite continued fractions \(\displaystyle{A}={1}+{d}{\frac{{{1}}}{{{1}+{\frac{{{1}}}{{{1}+{\frac{{{1}}}{{\ddots}}}}}}}}}\backslash{B}={2}+{d}{\frac{{{1}}}{{{2}+{\frac{{{1}}}{{{2}+{\frac{{{1}}}{{\ddots}}}}}}}}}\) Given the two

meiprate81w

meiprate81w

Answered question

2022-03-18

Comparing 2 infinite continued fractions
A=1+d11+11+1

B=2+d12+12+1
Given the two infinite continued fractions A and B above, which is larger, 2A or B?

Answer & Explanation

Dixie Klein

Dixie Klein

Beginner2022-03-19Added 3 answers

An alternative approach
A=1+d11+11+1<1+d11=2
B=2+d12+12+1>2
Showing A<B
Thus 2A=2+d2A>2+d22=3
B=2+d1B<2+d12
showing 2A>B.

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