Posts by zahlenspieler

zahlenspieler · Euler Avenue

Hi, actually I learned that not today but some 35 years ago or so: The curve given by

is actually a hyperbola with foci

zahlenspieler · Euler Avenue

Let r be a real number; and J^2=-1. Then

and

Thus

In my proof I didn't use any extension of the exponential function to complex numbers; but just some (very rough) estimates for

etc.

zahlenspieler · This is Cool

Mcbattle wrote:

Yes that is it. Or to make it easier it is the sum of the last two numbers in the sequence.

Hi Mcbattle, I've just finished an inductive proof of your claim: Let

, and if . Then
, and

for all integers .

(the 2nd statement is needed to complete the induction step.)
Furthermore, you need

.
I guess the easiest way is to use the Euler-Binnet formula; with a little more work, it can be proved without it.

Regards,
zahlenspieler

zahlenspieler · Guestbook

glenn101 wrote:

Algebra really isn't too difficult, constant revision is key to success but then I guess I can say that about ALL areas of maths:P

Hi glenn101, well I guess then you've not got in contact with the really hard stuff like measure theory, algebraic geometry/topology etc.? Good luck,
zahlenspieler

zahlenspieler · Help Me !

Hi everyone!
It all started when I proved

.
Let ,
where r is some real number.
Now I would like to show that ,
where .
So I proved the following inequality for positive integers :
.

Expanding

gives
.
As n grows towards infinity, the binomial coefficients go to . Now taking the absolute values, that sequence is bounded above by .

But now I got stuck. One idea that I have is the sandwich theorem -- i.e. to 'squeeze' the sequence of partial sums of the cosine series between that sequence above and another sequence

.

The trouble is the altering signs, so I just can't add up inequalities ...
Any ideas?
Regards,
zahlenspieler

zahlenspieler · Introductions

Hi! As my username suggests, I'm fond of numbers -- I started studying math but then I quit; nevertheless I still do it as a hobby. I gess most I like number theory -- though I've not gotten very far -- whereas algebra and other stuff: Oh leave me alone with it!
So I hope that I get the 'fun' part back -- at least I do when experimenting. Or when I finally finished a proof.
Besides, I'm interested in the history of math.
Until next time ...

Math Is Fun Forum

#1 Re: Euler Avenue » What had you learned today that you found interesting? » 2018-11-14 14:53:18

#2 Euler Avenue » Sine and cosine » 2018-10-02 09:24:54

#3 Re: This is Cool » Something I found about the Fibonacci sequence » 2018-05-08 06:56:27

#4 Re: Guestbook » Don't Post here! » 2018-05-08 03:40:00

#5 Help Me ! » Towards a proof of Euler's formula » 2018-04-12 22:59:10

#6 Introductions » Short intro » 2018-04-12 22:18:09

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