The Fibonacci sequence starts with the terms 1,1 and then proceeds by letting the next term be the sum of the previous two terms. So the sequence starts \(1,1,2,3,5,8,13,21,34, \ldots\). With this in mind, consider the decimal expansion of \(x=\frac{100}{9899}\) : it is \(0.010102030508132134 \ldots\) Note how the Fibonacci sequence lives inside this expansion. Can you explain this? Do you think it continues forever?