Question

A) Give the definition of Cauchy sequence. Then give an example.

Answer 1

Answer:

Step-by-step explanation:

In mathematics a Cauchy sequence is a sequence whose elements become closer for larger n.

i.e. for a sequence $x_1, x_2,...x_n$

if $|x_n-x_m|$ for all m,n >n then we call this a cauchy sequence.

eg:

$x_1 =1, x_{n+1} =1+\frac{1}{x_n}$

This will be of the form

$1,2,3/2, 5/3, 8/5, 13/8,.....$

For large n, the difference between consecutive terms would be very small.