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**1. Homework Statement**

3. (10 points) Show that if {xn}, {yn} are two sequences of positive real

numbers then

lim (xn +yn)^(1/n) is the max of lim(xn)^(1/n) and lim(yn)^(1/n)

provided these limits exist.

**2. Homework Equations**

Does anyone have any nice inqualities or tricks?

**3. The Attempt at a Solution**