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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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 …

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 = …

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 …

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What is interesting is that your formula is the closed form for a different summation, i.e. $\displaystyle \sum_ {i=0}^n \binom {i+1}2=\sum_ {i=0}^n \frac {i (i+1)}2=\frac {n (n+1) …

How can we sum up $\sin$ and $\cos$ series when the angles are in arithmetic progression? For example here is the sum of $\cos$ series: $$\sum_ {k=0}^ {n-1}\cos (a+k \cdot d) =\frac {\sin (n …

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.

Dec 28, 2014 · How would I estimate the sum of a series of numbers like this: $2^0+2^1+2^2+2^3+\\cdots+2^n$. What math course deals with this sort of calculation? …