I was trying to prove that during reflection from a concave mirror, all rays parallel to the principal axis will meet the principal axis at a point (focus) that is equidistant from the centre of curvature and the pole. I thought of proving this using coordinate geometry (and some trigonometry). I...

Now, this question looks simple, it did to me too, at first, but I got stuck at a point and can't get out. This is how I did it, take a look : $$\dfrac{a^{n+1}+b^{n+1}}{a^n+b^n}=\dfrac{a+b}{2}$$ By cross multiplication, we get : $$2a^{n+1}+2b^{n+1}=(a+b)(a^n+b^n) = a^{n+1}+b^{n+1}+ab^n+a^nb$$ ...