# Convergent Series Problem

1. Jan 2, 2013

1. The problem statement, all variables and given/known data
Let Ʃ from n=1 to ∞ an and Ʃ from n=1 to ∞ bn be convergent series, with an$\geq$0 and bn$\geq$0 for all n$\in$$N$. Show that the series Ʃ from n=1 to∞ max(an,bn) converges.

2. Relevant equations
I'm guessing it's got something to do with the cauchy criterrion for convergence of series but I'm not sure where to begin? Any hints would much appreciated

2. Jan 2, 2013

### lurflurf

I would write

2 max(a,b)=a+b+|a-b|

or

max(a,b)<=a+b

Either of which obviously converge.