Proving Convergence of Sum(a_n)^2: Examples & Explanation

[fk378]

Homework Statement

Prove that if a_n>or equal to 0, and sum(a_n) converges, then sum(a_n)^2 also converges.

The Attempt at a Solution

The only example I can think of is 1/(n^p) where p is any exponent greater than 1. Are there any other examples that I can use or do I only need to use this example to prove it?

 

[jhicks]

I don't think you can prove something by example.

 

[Dick]

If sum(a_n) converges then there must be an N such that for n>=N, a_n<=1, right? sum(a_n) for n>=N converges. Do a comparison test between a_n and a_n^2 for n>=N.