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 ...

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, …

Explore related questions elementary-number-theory summation See similar questions with these tags.

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 …

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Dec 11, 2014 · Rules for Product and Summation Notation Ask Question Asked 12 years, 1 month ago Modified 6 years, 2 months ago

Mar 7, 2016 · More specifically, I do not understand the condition on the summation: $$\sum_ {i>j}$$ Does this actually mean sum over both i and j, using only values of i that satisfy i>j ?

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

The first chapter of Concrete Mathematics by Graham, Knuth, and Patashnik presents about seven different techniques for deriving this identity, so you might be interested to look at that.

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 $\\sum_{i=1}^n i+(x-1)$.