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prove-that-a-b-n-a-n-b-n-lt-2-n-1-n-gt-1-n-natural-




Question Number 61532 by maxmathsup by imad last updated on 04/Jun/19
prove that   (((a+b)^n )/(a^n  +b^n )) <2^(nāˆ’1)      āˆ€ n>1    (n natural)
$${prove}\:{that}\:\:\:\frac{\left({a}+{b}\right)^{{n}} }{{a}^{{n}} \:+{b}^{{n}} }\:<\mathrm{2}^{{n}āˆ’\mathrm{1}} \:\:\:\:\:\forall\:{n}>\mathrm{1}\:\:\:\:\left({n}\:{natural}\right) \\ $$

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