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 …

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

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 …

Jul 9, 2014 · $ \\sum_{i=0}^{5}{i^2} = 0^2+1^2+2^2+3^2+4^2+5^2 = 55 $ How to write this Sigma notation only for odd numbers: $ 1^2+3^2+5^2 = 35 $ ?

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.

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 …