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summation - The idea behind the sum of powers of 2 - Mathematics Stack . . . I know that the sum of powers of 2 2 is 2n+1 − 1 2 n + 1 1, and I know the mathematical induction proof But does anyone know how 2n+1 − 1 2 n + 1 1 comes up in the first place For example, sum of n numbers is n(n+1) 2 n (n + 1) 2 The idea is that we replicate the set and put it in a rectangle, hence we can do the trick What is the logic behind the sum of powers of 2 2 formula?
summation - How to prove a formula for the sum of powers of $2$ by . . . Your induction hypothesis and what you are trying to prove for induction are both incorrect What you are trying to prove is that the sum of the powers of 2 2 up to n n is equal to 2n+1 − 1 2 n + 1 − 1 So your inductive hypothesis should be that this result is true for k k; that is, that
summation - Rules of Double Sums - Mathematics Stack Exchange What are the (most important) rules of double sums? Below are some rules I encountered - are they all correct and complete? Offerings of clear intuition or proofs (or other additions) are most welc