Question

What does it mean for a sequence (sn) to satisfy the Cauchy criteria?

A. Lim |sn+1 - sn| = 0.
B. Lim |sn+1 - sn| = [infinity].
C. Lim |sn+1 - sn| exists.
D. Lim |sn+1 - sn| does not exist.

Answer 1

A sequence (sn) satisfies the Cauchy criteria if the limit of the difference between consecutive terms of the sequence goes to zero.

Step-by-step explanation:

In mathematics, a sequence (sn) satisfies the Cauchy criteria if the limit of the difference between consecutive terms of the sequence goes to zero. This can be expressed as:

Lim |sn+1 - sn| = 0

Option A is the correct answer.