Thread: Positive Sequence with Positive Limit

Suppose that sn is a sequence of positive numbers converging to a positive limit L. Show that there is a c > 0 such that sn > c for all n.

I can do this for sn < c using the limit definition, but I don't know how to show this.

Originally Posted by veronicak5678

Suppose that sn is a sequence of positive numbers converging to a positive limit L. Show that there is a c > 0 such that sn > c for all n.

I can do this for sn < c using the limit definition, but I don't know how to show this.

First of all either learn to use LaTeX or do not use special fonts.

Suppose that .
Using and the definition of sequence convergence prove that there is a p.i. N such that .

Now let .

You are done if you fill in the details.