Solution to De Moivre's Theorem w/ q=E(Φ)

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Homework Statement



Find what the following formula yields if we substitute q= E(Φ)

the formula is:1+2q+3q^2+...+nq^n-1=(1-(n+1)q^n+nq^n+1)/(1-q^2)



Homework Equations





The Attempt at a Solution



i substituted Φ in for q:

1+2E( Φ)+3E( Φ)^2+...+nE( Φ)^n-1= (1-(n+1)E( Φ)^n +nE( Φ)^n+1)/(1-E( Φ)^2)

now I'm not sure where to go next
 
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What is E(Φ) supposed to be??
 
e of phi
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

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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