Induction Proof for Sum of First n Powers of 2 (2^0 + 2^1 + ... + 2^n = 2^(n+1) - 1)

We prove the sum of powers of 2 is one less than the next powers of 2, in particular 2^0 + 2^1 + ... + 2^n = 2^(n+1) - 1. In the lesson I will refer to this as "the sum of the first n powers of 2", but note it is actually the first n+1 powers of 2 because 2^0 is included. Saying "the first n powers of 2" is just to explain we're going from 2^0 to 2^n in our sum. We'll prove this result using mathematical induction, and it's quite straightforward. We get some additional insight into the sum of powers of 2 using binary representations. #Proofs

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