Question

Define a series that satisfies the Cauchy criterion.

A. A series with decreasing terms.
B. A series with bounded terms.
C. A series where the sum of differences of consecutive terms approaches zero.
D. A series with alternating terms.

Answer 1

A series satisfies the Cauchy criterion if the sum of the differences of consecutive terms approaches zero.

Step-by-step explanation:

According to the Cauchy criterion, a series is said to satisfy the criterion if the sum of the differences of consecutive terms approaches zero. This means that as we add more and more terms to the series, the difference between consecutive terms becomes smaller and smaller. So, the correct option is C.