To show that converges uniformly to on , we have to show there exists an N such that for all x in the interval and ,

I'm sorry I'm a bit rusty, but perhaps it would help to note that you can consider an upper bound for your positive sequence . If the least upper bound for is a real number, say M, then you can say and for all n. If there is no least upper bound for your positive sequence, I'm not sure how to continue.