The Fibonacci sequence begins with 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ... with each new term formed by adding the two preceding ones.
The "Modonacci" number M is formed by starting with a decimal point, and then appending the last digit of each entry in the Fibonacci sequence.
Thus, the first ten decimal places are:
M = 0.1123583145...
Puzzle 1: Prove that M is a rational number.
Puzzle 2: Since M is a rational number, it can be written as a ratio P/Q, where P and Q are integers with no common factor. What are the values of P and Q?
I give up, show me the solution.
This puzzle was kindly supplied by Scott Hansen.