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HMMT 2015 Algebra #3 본문

HMMT/2015

HMMT 2015 Algebra #3

수악중독 2015.03.15 08:39

Let P be a real number and \(c \ne 0\) an integer such that\[ c-0.1 < x^p \left ( \dfrac{1-(1+x)^10}{1+(1+x)^10} \right ) < c+0.1 \] for all (positive) real numbers \(x\) with \(0<x<10^{-100}\). (The exact value \(10^{-100}\) is not important. You could replace it with any "sufficiently small number".) Find the ordered pair \((p, \;c)\). 






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