Hi I'm doing a small induction proof for bernoullis inequailty:(adsbygoogle = window.adsbygoogle || []).push({});

Proof:

Given the inequality [tex]A(n) = (1+x) ^n \geq 1+nx[/tex]

[tex]r \geq -1[/tex], [tex]n \in \mathbb{N}[/tex]

Initial step:

A(n=1) is true cause [tex](1+x) \geq 1 + x[/tex] is true.

Induction step:

A(n) is true is since n = 1 and [tex]r \geq -1[/tex] so

[tex]0 \geq 0[/tex]

Therefore by the rules of induction

A(n+1) is true.

q.e.d.

Is my proof sufficient ??

Best Regards,

Bob

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# Bernoulli inequality proof

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