How do I calculate this sum in terms of 'n'? I know this is a harmonic progression, but I can't find how to calculate the summation of it. Also, is it an expansion of any mathematical function? 1 ...

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Feb 23, 2021 · Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant …

Mar 8, 2015 · How do I prove this by induction? Prove that for every natural number n, $ 2^0 + 2^1 + ... + 2^n = 2^{n+1}-1$ Here is my attempt. Base Case: let $ n = 0$ Then, $2^{0+1} - 1 = 1$ Which is true.

Oct 29, 2016 · I know that the sum of powers of $2$ is $2^{n+1}-1$, and I know the mathematical induction proof. But does anyone know how $2^{n+1}-1$ comes up in the first place. For example, …

Sep 2, 2017 · $\\sum_{i=1}^n i$ is the same as $\\frac{n(n+1)}{2}$. Can someone explain how the sigma notation is converted to this? I'm trying to figure out if there's a way to convert $\\sum_{i=1}^n i+(x-1)$.

Feb 25, 2015 · Rules for Product and Summation Notation Ask Question Asked 12 years, 1 month ago Modified 6 years, 2 months ago

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Possible Duplicate: How do I come up with a function to count a pyramid of apples? Proof that ∑ k=1n k2 = n(n+1)(2n+1) 6 ∑ k = 1 n k 2 = n (n + 1) (2 n + 1) 6? Finite Sum of Power? I know that the sum …

Apr 3, 2021 · Repeated sum is denoted using $\\sum$ and is called "summation." What is the name for the analogous process with multiplication, denoted $\\prod$?