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...
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) =...
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.
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...