Finite Continued Fractions Quiz

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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</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</p> Signup and view all the answers