Thread: sequence question
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Old November 14th, 2007, 10:34 AM
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Originally Posted by PvtBillPilgrim View Post
Could someone show me what to do here:
For each positive integer n, let fn be the function defined by
fn(x) = x^2n + x^(2n−1) + ... + x^2 + x + 1. Let mn be the minimum of fn on the interval [−1,0]. Prove that the sequence (mn) converges to a limit A and then find A.

Thank you for your help.
We can wrtite x^{2n}+x^{2n-1}+...+x+1 = \frac{1-x^{2n+1}}{1-x} \mbox{ if }x\not = 1 \mbox{ and }2n+1 \mbox{ if } x=1. So the mimmum occurs for zero for all n.

I think you missted something because it is not a very interesting problem.
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