3 ms·
The Remarkable Number 1/89 (2004)
- impendia 7y agoThis works because of generating functions: You can check that 1/(1 - x - x^2) = 1 + x + 2x^2 + 3x^3 + 5x^4 + 8x^5 + 13x^6 + 21x^7 + ... To check this (not totally rigorously), multiply both sides by 1 - x - x^2 and multiply everything out. On the right side the recurrence relation implies that everything but the first term will cancel out. So you can also get, for example, 1/9899 = 0.0001010203050813213455... 1/998999 = 0.000001002003005008013021034055089144233... and so on.