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 …

Feb 23, 2021 · I am trying to help a high school student to solve summation calculation problems. The i i value of most answers I found was based on i = 1 i = 1 like this: Now, the i i value of our questions is …

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

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.

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 …

Aug 21, 2012 · What is the relation between a summation and an integral ? This question is actually based on a previous question of mine here where I got two answers (one is based on summation …

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 …

[Math Processing Error] ∑ k = 1 n k 2 = ∑ k = 1 n k (k + 1) k = n (n + 1) (n + 2) 3 n (n + 1) 2 = n (n + 1) (2 n + 1) 6 I like to use this because the general sum involving p p can be derived as a combination …