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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 - 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
summation - Proving by induction that $ \sum_ {k=0}^n {n \choose k} = 2 . . . You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do I get it? Instead, you can save this post to reference later