Solve Recurrence Relation: A0,A1,A2 Given

swtlilsoni
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Homework Statement



An=3An-2-2An-3

When
A0=3
A1=1
A2=8

I tried to solve it normally like a normal recurrence relation however since it is not A sub n-1, it turns into a polynomial where the variable is raised to the third power which I couldn't factor and the whole thing turned into a mess.
 
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welcome to pf!

hi swtlilsoni! welcome to pf! :smile:

you mean x3 - 3x + 2?

can't you see one obvious root, just from looking at it? :wink:
 

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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