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.

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- Aug 17th 2011, 03:00 PMveronicak5678Positive 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.

- Aug 17th 2011, 03:27 PMPlatoRe: Positive Sequence with Positive Limit
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.