{"ops":[{"attributes":{"bold":true},"insert":"DO NOT BE FOOLED BY THE FIRST FEW TERMS! "},{"insert":"\n\n"},{"attributes":{"color":"#000000"},"insert":"Mathematics is often described as the study of patterns. So the most basic mathematical question you might ask could be, well, how do I know a pattern when I see one? For a pattern to be interesting, we want there to be a simple rule that allows us to predict how some process will behave. The simplest examples are rules for generating sequences of numbers – (i) to get the next even number, we just add two; {ii) to get the next Fibonacci number, we add the previous two numbers in the sequence together; (iii) to get the("},{"attributes":{"color":"#000000","italic":true},"insert":"n"},{"attributes":{"color":"#000000"},"insert":"+1)"},{"insert":"th square number we can add 2"},{"attributes":{"color":"#000000","italic":true},"insert":"n"},{"attributes":{"color":"#000000"},"insert":"+1 "},{"insert":"to the "},{"attributes":{"color":"#000000","italic":true},"insert":"n"},{"attributes":{"color":"#000000"},"insert":"th"},{"insert":"\n"},{"attributes":{"color":"#000000"},"insert":"... We can check that these patterns work for "},{"attributes":{"color":"#000000","italic":true},"insert":"n"},{"attributes":{"color":"#000000"},"insert":"=1"},{"insert":"\n, and then for "},{"attributes":{"color":"#000000","italic":true},"insert":"n"},{"attributes":{"color":"#000000"},"insert":"=2"},{"insert":"\n, and for "},{"attributes":{"color":"#000000","italic":true},"insert":"n"},{"attributes":{"color":"#000000"},"insert":"=3"},{"insert":"\n, and at that point it's tempting to just say, well, it must keep on going, right?\n\nKeep reading this interesting article \""},{"attributes":{"link":"https://nrich.maths.org/7665"},"insert":"On the Importance of Pedantry"},{"insert":"\" \n\n\n"}]}