#1795 · Number Theory · Diophantine equations

Fifth convergent of a continued fraction

Prove that $9 a^{2} + 3 = 3 a + \frac{1}{2 a +} \frac{1}{6 a +} \frac{1}{2 a +} \frac{1}{6 a +} \dots\dots$ , and find the fifth convergent.

~15 minAnswer checked instantlycontinued fractionsconvergents

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXVII. Recurring Continued Fractions, Examples XXVII.b, No. 7

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Checked against the answer in H. S. Hall & S. R. Knight, Higher Algebra (1891).