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Line 1: {{draft task}}A number may be represented as a continued fraction (see http://mathworld.wolfram.com/ContinuedFraction.html) as follows: :<math>cf = a_1 + \cfrac{b_1}{a_2 + \cfrac{b_2}{a_3 + \cfrac{b_3}{\mathrm{etc\ldots}}}}</math> ~~[[Image:Continued_Fraction.PNG\|center\|Continued Fraction\|200px]]~~ The task is to write a program which generates such a number and prints a real representation of it. The code should be tested by calculating and printing the square root of 2, Napier's Constant, and Pi. For the square root of 2, bN<math>b_N</math> is always <math>1</math>. a1<math>a_1</math> is <math>1</math> then aN<math>a_N</math> is <math>2</math>. For Napier's Constant, a1<math>a_1</math> is <math>2</math>, then aN<math>a_N</math> is <math>N-1</math>. b1<math>b_1</math> is <math>1</math> then bN<math>b_N</math> is <math>N-1</math>. For Pi, a1<math>a_1</math> is 3 then aN<math>a_N</math> is always <math>6</math>. bN<math>b_N</math> is <math>(2N-1)(2N-1)</math>. =={{header\|Python}}== <lang python># The continued Fraction▼ ~~<lang python>~~ ▲# The continued Fraction def CF(a, b, t): if 0 < t: Line 86 ⟶ 82: cf = CF(Pi_a(), Pi_b(), 950) print(pRes(cf, 10)) #3.1415926532</lang> ~~</lang>~~

Continued fraction: Difference between revisions

Continued fraction (view source)