Solving Algebraic Equations: Need Help?

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Homework Statement




Please see attached

Homework Equations





The Attempt at a Solution



Not sure how to begin actually...

I've tried taking logs of both sides and using sterling's approximation but it came to nothing... :(

Any ideas? Thanksss
 

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any ideas anyone?
 
They are using things like (N/2+m)!/(N/2)!=(N/2+m)*(N/2+(m-1))*...*(N/2+1). Expand the right side keeping only the two highest powers of N/2. You get (N/2)^m+(m+(m-1)+...+2+1)*(N/2)^(m-1).
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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