Question

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

Answer 1

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|<\epsilon` for all m,n >n then we call this a cauchy sequence.

eg:

`x_1 =1, x_(n+1) =1+(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.