Prove 2n^n ≤ (n+1)^n...?

Using Bernoullis inequality

(1+a)^n ≥ 1+na for a>0

prove that 2n^n ≤ (n+1)^n.

Can anyone help please??

1 Answer

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  • Indica
    Lv 7
    8 years ago
    Best answer

    Set a=1/n in (1+a)^n ≥ 1+na to get (1+1/n)^n ≥ 1+n(1/n) = 2

    Multiply by n^n : (n+1)^n ≥ 2n^n

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