Question

What is the upper bound of the infinite sequence 1/x^2, where xE{R\0}

We know that x={1, 1/4, 1/9, 1/16,.....}
Since all x here are greater than 0 or less than equal to 1.

Can't we take 1 as an upper bound here(My tutorial instructor has mentioned so in an answer sheet) I'm confused. Can someone explain? Thanks!

Answer 1

Clearly 1 is the least upper bound, since all of the other terms are less than 1, and in fact the largest term is exactly 1.

Answer 2

Thank you very much!