4. Prove that the terms of the sequence $\displaystyle U_n = n^{2}-10n+27$ are positive. For what value of $\displaystyle n$ is $\displaystyle U_n$ smallest?
How do I do this?
Well first, n = 0 for $\displaystyle U_n$ to be the lowest, because any negative numbers squared would turn out positive, 0 is smaller than any positive number, so to answer your question n = 0. Im not sure how to prove that they are positive, but I think it has something to do with squaring, anytime you square a negative it becomse positive, and -10 times any negative number will become positive.