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.
Is what you did correct?
f_n+1(x) - f_n(x) is decreasing (I believe). This should imply that (m_n) is decreasing. And it is bounded by [-1,0] so it must be convergent.
As n goes to infinity, f_n(x) goes to 1/(1-x) on (-1,0]. How do I find the limit A though (to what (m_n) converges)?
Thanks for your help.