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Question Number 386 by 123456 last updated on 25/Jan/15

p_{n + 1} = p_{n} + q_{n}

q_{n + 1} = p_{n} q_{n}

p_{0} = 2

q_{0} = 3

f (x) = \frac{p_{0}}{q_{0}} + \frac{p_{1}}{q_{1}} x + \frac{p_{2}}{q_{2}} x^{2} + \frac{p_{3}}{q_{3}} x^{3}

f (\frac{2}{3}) = ?

Answered by prakash jain last updated on 27/Dec/14

p_{1} = 5, q_{1} = 6

p_{2} = 11, a_{2} = 30

p_{3} = 41, q_{3} = 330

f (\frac{2}{3}) = \frac{2}{3} + \frac{5}{6} \times \frac{2}{3} + \frac{11}{30} \times \frac{4}{9} + \frac{41}{330} \times \frac{8}{27}

= \frac{110 \times 27 \times 2 + 345 \times 10 + 33 \times 44 + 41 \times 8}{27 \times 330}

= \frac{5940 + 3450 + 1452 + 328}{27 \times 330} = \frac{11170}{8910} = \frac{1117}{891}