Question

prove that a sequence is a convergent sequence if and only if it is a cauuchy sequence?​

Answer 1

Step-by-step explanation:

1. Every convergent sequence (with limit s, say) is a Cauchy sequence, since, given any real number ε > 0, beyond some fixed point, every term of the sequence is within distance ε/2 of s, so any two terms of the sequence are within distance ε of each other