Finite Continued Fractions Quiz

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Questions and Answers

Which of the following best describes a finite continued fraction?

  • An expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then terminating after finitely many steps (correct)
  • An expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then terminating after infinitely many steps
  • An infinite expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number
  • An expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then continuing indefinitely

What is the general assumption about the numerator of all fractions in a continued fraction?

  • The numerator of all fractions is an integer
  • The numerator of all fractions is 1 (correct)
  • The numerator of all fractions is an arbitrary value
  • The numerator of all fractions is 0

What are the coefficients or terms of a continued fraction?

  • The integers in the sequence, excluding the first
  • The integers in the sequence, other than the first (correct)
  • The integers in the sequence, including the first
  • The integers in the sequence, excluding the first and the last

What is an infinite continued fraction?

<p>An infinite expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number (A)</p> Signup and view all the answers

What is a generalized continued fraction?

<p>An expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, with arbitrary values and/or functions used in place of one or more of the numerators or the integers in the denominators (D)</p> Signup and view all the answers

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