freeCodeCamp

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id	challengeType	title	forumTopicId
5900f3a51000cf542c50feb8	5	Problem 57: Square root convergents	302168

Description

It is possible to show that the square root of two can be expressed as an infinite continued fraction. √ 2 = 1 + 1/(2 + 1/(2 + 1/(2 + ... ))) = 1.414213... By expanding this for the first four iterations, we get: 1 + 1/2 = 3/2 = 1.5 1 + 1/(2 + 1/2) = 7/5 = 1.4 1 + 1/(2 + 1/(2 + 1/2)) = 17/12 = 1.41666... 1 + 1/(2 + 1/(2 + 1/(2 + 1/2))) = 41/29 = 1.41379... The next three expansions are 99/70, 239/169, and 577/408, but the eighth expansion, 1393/985, is the first example where the number of digits in the numerator exceeds the number of digits in the denominator. In the first one-thousand expansions, how many fractions contain a numerator with more digits than denominator?

Instructions

Tests

tests:
  - text: <code>euler57()</code> should return 153.
    testString: assert.strictEqual(euler57(), 153);

Challenge Seed

function euler57() {
  // Good luck!
  return true;
}

euler57();

Solution

// solution required

1.3 KiB Raw Blame History