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## Homework Statement

[tex] X \geq Y > 0, find \lim_{n \to \infty} \left(\frac{2X^n + 7Y^n}{2}\right)^{1/n}

[/tex]

## Homework Equations

## The Attempt at a Solution

I'm not really sure how to do it, but i guess I need to use the fact that [tex] \frac{Y}{X} \leq 1 [/tex], and so [tex] \lim_{n \to \infty} \left(\frac{Y}{X}\right)^n = 0. [/tex]

Thanks for your help.