Pointwise convergence of (x^n)/(1 + x^n)

[youko.shi]

Homework Statement

Find the function that (x^n)/(1 + x^n) converges to as n goes to infinity, on the interval [0,2]

Homework Equations

The Attempt at a Solution

I've worked out the fact that on the interval [0,1) it converges to 0, and when x is 1 it converges to 1/2, but for the life of me I'm not sure what the first step of proving what it converges to on the (1,2] interval. hints?

 

[Dick]

Divide numerator and denominator by x^n. Now can you figure out what it converges to on (1,2]?

 

[youko.shi]

Yes! It becomes 1 / ( 1/(x^n) + 1), which goes to 1 / (0+1) = 1.

Thank you so much :)