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: n − 1 ∑ k = 0cos(a + k ⋅ d) = sin(n × d 2) sin(d 2) × cos …

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.

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 …

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

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

isn't the double summation notation a little less confusing? Or at least worthwhile mentioning what is meant by \sum_ {i\neqj}?

Aug 4, 2018 · The following proof is from Apostol's book: Questions: On the first line of the proof, he uses '{}' just as brackets or do they have other meaning like $[x]$ being the floor function? …