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 …

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 …

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.

Mar 3, 2018 · In the second notation, a specific summation order is given, whereas in the first one there isn't. So the first notation is only appropriate if the order of summation doesn't matter.

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 …

Sep 13, 2015 · as a product of sums. (In this answer we assume that the index sets, I, J, etc., are finite, though with some care we can extend them to infinite sets under suitable conditions.) …

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 …

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