A Golden Fraction II

Number Theory Level 4

\[0.1123101\ldots\]

Consider a decimal such that the \(n^{\text{th}}\) digit to the right of the decimal place is the \(n^{\text{th}}\) term of the Fibonacci Sequence \(\mod 4\), as shown above.

The exact value of this decimal can be expressed in the form \(\dfrac{a}{b}\) for coprime positive integers \(a\) and \(b\).

What is the value of \(a+b\)?

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 5 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.