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Never mind--figured it out.

This is something that comes up when I want to determine whether the sequence of functions {f_n} converge uniformly to f: Suppose f_n(x) = sqrt(x^2 + 1/n^2), so f(x) = x. Then, according to Spivak, f(x) - f_n(x) = sqrt(x^2) - sqrt(x^2 + 1/n^2) = 1/(2n^2*sqrt(ε)) for some ε such that x^2 < ε...

If n>m>1, find upper and lower bounds for n!/m! Answer: upper bound = {[(n+1)^(n+1)]/[(m+1)^(m+1)]}*e^(-(n-m)) lower bound = [(n^n)/(m^m)]*e^(-(n-m)) This is from a chapter on finding bounds for sum of series. Can someone please explain how to arrive at the answer? Thanks!

Yes it was a typo. And yes I'm required to use that result! :rolleyes:

I wanted to post this in the homework forum, but there's only pre-calc for math. Question: Show that i*r^i-(i-1)*r^(i-1) = r^(i-1)-(1-r)i*r^i-1. Use this result to find the sum of i*r^(i-1) from i=1 to i=n. I've done the first part of this question, but need some help with the second. Thanks!