i got this question when i read the proof of stone-weierstrass theorem in baby rudin , page 159 , this inequality seems right when n becomes larger, since 1-nx^2 would be negative and (1-x^2)^n always positive, but i don't know how to proved it rigorously using binomial theorem for all n , or is there any other rigorous proof ?(adsbygoogle = window.adsbygoogle || []).push({});

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# HELP how to prove (1-x^2)^n >= 1-nx^2 when x belongs to the interval [-1,1]?

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