Question

A sequence (Sn) in R

2 where Sn = (sn, tn), n ∈ N converges in R

2

iff​

Answer 1

Answer:

tn = √ t, if tn ≥ 0 for all n ∈ N. Proof: By Fact 2, we have |sn − s| → 0, and |tn − t| → 0, as n ... (Cauchy test for convergence) A sequence in R is convergent iff it.