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1. Limit of factorial functions

Homework Statement Show that the folowing holds: \lim_{n\to\infty} \frac{(n!)^2 4^n}{(2n)!} = \infty Homework Equations It can be shown that \frac{(n!)^2 4^n}{(2n)!} = \prod_{k=1}^n \frac{4k}{k+n} The Attempt at a Solution If I can proove that \lim_{n\to\infty} \ln\left[\frac{(n!)^2...
2. Reformulating exact values

Homework Statement Find exact values for z without any trigonometrical components or imaginary numbers x = \frac{79}{60} + \frac{1}{30} \sqrt{6121} cos\left(\frac{1}{3}arccos(z)\right) where z = \frac{473419}{6121\sqrt{6121}} Homework Equations cos\left(\frac{1}{3}arccos(z)\right) =...
3. Correlation between science and atheism/agnosticism

I am searching for correlation with science and atheism/agnosticism. If this thread conflict with the rules (which I don't think it does), I accept that. If so, just remove it. If allowed: Discuss the correlation between science and atheism/agnosticism.
4. Solving 2 equation with 2 variables (hard)

[PLAIN]http://folk.ntnu.no/jonvegar/images/math.gif [Broken] I really need some help here (no program is allowed :smile:)
5. Solve cos((1/3)*arccos(x))

Homework Statement Find an albebraic expression for cos((1/3)*arccos(x)), in order to get rid of the trigonometric operands. Homework Equations cos(arccos(x))=x The Attempt at a Solution cos(x)= 4cos(x/3)^3 - 3cos(x/3), I can reduce cos(cos(x)/3) by noting that cos(arccos(x))=x...