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Using-the-principle-of-mathematical-induction-to-prove-that-a-1-a-2-a-n-a-1-a-2-a-n-n-a-1-a-2-a-n-1-n-




Question Number 88458 by TawaTawa1 last updated on 10/Apr/20
Using the principle of mathematical induction to prove  that   a_1  ,   a_2  ,  ... , a_n  ,  ((a_1  + a_2  + ... + a_n )/n)    ≥   ((a_1  ,  a_2  ,  ... , a_n ))^(1/n)
$$\mathrm{Using}\:\mathrm{the}\:\mathrm{principle}\:\mathrm{of}\:\mathrm{mathematical}\:\mathrm{induction}\:\mathrm{to}\:\mathrm{prove} \\ $$$$\mathrm{that}\:\:\:\mathrm{a}_{\mathrm{1}} \:,\:\:\:\mathrm{a}_{\mathrm{2}} \:,\:\:…\:,\:\mathrm{a}_{\mathrm{n}} \:,\:\:\frac{\mathrm{a}_{\mathrm{1}} \:+\:\mathrm{a}_{\mathrm{2}} \:+\:…\:+\:\mathrm{a}_{\mathrm{n}} }{\mathrm{n}}\:\:\:\:\geqslant\:\:\:\sqrt[{\mathrm{n}}]{\mathrm{a}_{\mathrm{1}} \:,\:\:\mathrm{a}_{\mathrm{2}} \:,\:\:…\:,\:\mathrm{a}_{\mathrm{n}} } \\ $$

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