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Alternating multiplier recurrence for convergents of the square root of eleven

If

p_{n} / q_{n}

are the convergents of

11

, then

p_{n + 1} + q_{n + 1} 11 = ⎩ ⎨ ⎧ (3 + 11) (p_{n} + q_{n} 11), \frac{3 + 11}{2} (p_{n} + q_{n} 11), n odd, n even .

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