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 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 …

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 …

Jan 28, 2022 · This seems pretty basic, but I'm starting with the subject and the only formula I have to use for these kind of problems starts the summation at 1, like this. ∑n i=1(i) ∑ i = 1 n (i) = n(n+1) 2 n …

Interchanging summation and differentiation is possible if the derivatives of the summands uniformly converge to 0, and the original sum converges. This follows from the equivalent criterion for …

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

Taking differences once give i2 i 2, again gives 2i − 1 2 i 1, and a third time gives a constant 2 2. This suggests the formula should be a third-degree polynomial with leading coefficient 2 3! = 1 3 2 3! = 1 …

You ask why this nontraditional approach to summation might be useful. The answer is that sometimes this approach gives the correct result in a real world problem. A simple example is the Casimir effect. …

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.

Easy way of memorizing or quickly deriving summation formulas Ask Question Asked 10 years, 1 month ago Modified 5 years ago