Question

O0 (9) Suppose we make the following definition: A sequence Iny is said to be pleasant if for every є 〉 0 th l4m-Yn| 〈 є whenever m,n 2 N. Prove that every convergent sequence is pleasant. Is every pleasant sequence in R convergent? If you answer is "yes," supply as good a justification as you can using only the ideas presented to this point and if your answer is "no," supply an example of a pleasant sequence which does not converge. ere is a positive integer N such that 79

Answer 1

"Let {q_n} be a convergent sequence Suppose q_n Rightarrow q as n Rightarrow infinity then given element > 0, n_elementof elementof N So in that