Number Theory – Almost Surely a Math Blog

Why does this fraction give the Fibonacci sequence? It’s no coincidence

July 28, 2022November 22, 2019 by VV

You may have seen one of the following viral math facts: The first fraction seemingly gives the Fibonacci numbers. That is, the sequence of numbers that starts with 1, then 1, then each successive term is the sum of the two prior terms. So the first few Fibonacci numbers are 1,1,2,3,5,8,13,21,… Which appear on the … Read more

The Harmonic Series and Friends

July 23, 2023October 26, 2019 by VV

A lot of times, math can be deceptive and unexpected A few examples are the Monty Hall problem, the Banach-Tarski paradox, and the Weierstrass function. Today we will look at one of the most famous and classic counterexamples, that is that if a sequence converges to zero, it’s series does not necessarily converge. What does … Read more