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Let a and b be the roots of \(7x^2 - x - 3 = 0\). Find \((1 + a + a^2 + a^3 + \dotsb)(1 + b + b^2 + b^3 + \dotsb).\)

Guest Feb 20, 2019

Guest · Answer 1 · 2019-02-21T12:57:22

Using quadratic formula, you get these 2 roots for your equation:

x = 1/14 (1 + sqrt(85)) and x = 1/14 (1 - sqrt(85))

But evaluating them as 2 sequences, both of them DIVERGE, because of 1 added at the beginning!. If you remove it, then they CONVERGE to -1