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Let a, b, c be positive real numbers suc...

Let a, b, c be positive real numbers such that `b^2- 4ac > 0` and let `alpha_1 = c`. Prove by induction that `alpha_(n+1)= (a alpha_n^2)/(b^2 -2a(alpha_1+alpha_2+...+alpha_n))` is well defined and `alpha_(n+1) ltalpha_n/2` for all `n = 1, 2, ..... `(Here, ‘well defined’ means that the denominator in the expression for `alpha_(n+1)`is not zero).

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