Posts Tagged ‘sequence’
The proof for the limit points of the sequence haven’t given me a calm dream untill today.
Of course the limit points of that sequence (almost intuitively)
Lemma.
Lemma proof.
from floor function definition web have the following inequality:
Now we will prove that
Let where
So we have
Let
so of course
Lets consider
and look closer [...]
Filed under: Mathematics, Science | 1 Comment
Tags: limit, points, sequence, sin, sin n, sinn
Reading some of the Lev Kourliandtchik books, I’ve found, kindy tricky observation how to write extreamly simple, this giant
with number of square roots.
It’s easy to dubunk that
and using that equality we have
cool, huh?
Filed under: Identity, Mathematics, Science | 4 Comments
Tags: 2, cos, cosinus, form, Identity, roots, sequence, short, square
Lets calculate more compilated sum
further, the last one equals to and now the first of the sums is equal to however the second one is easy, cause its a geometric sequence equal to under the law from previous post. Now we have , in the result of elementary algebraic transformation we [...]
Filed under: Mathematics, Methods | Leave a Comment
Tags: math, method, sequence, sum, upset, upseting
Asume that we want to calculate
Of course,
But the sum on the right side is equal to Therefore and so,
Filed under: Mathematics, Methods | Leave a Comment
Tags: geometric, math, method, sequence, sum
