Let P(n) be the statement that n!&lt;nn where n is an integer greater than 1. a) What is the statement P (2)? b) Show that P (2) is true, completing the basis step of the proof. c) What is the inductive hypothesis? d) What do you need to prove in the inductive step? e) Complete the inductive step. f) Explain why these steps show that this inequality is true whenever n is an integer greater than 1.

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Let P(n) be the statement that n!&amp;lt;nn where n is an integer greater than 1. a) What is the statement P (2)? b) Show that P (2) is true, completing the basis step of the proof. c) What is the inductive hypothesis? d) What do you need to prove in the inductive step? e) Complete the inductive step. f) Explain why these steps show that this inequality is true whenever n is an integer greater than 1.

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Let P(n) be&amp;nbsp;n!&amp;lt;nn&amp;nbsp;and n is an integer greater than 1.a) In the formula for P provided, change n to 2 (n).P(2) states&amp;nbsp;2!&amp;lt;22b)First of all2≠2&amp;lt;4=22P(2) is then noted to be true.c)A induction theory Suppose P(k) is true.k!&amp;lt;kkd) We must show that&amp;nbsp;P(k+1)&amp;nbsp;is &amp;nbsp;true.(k+1)!&amp;lt;(k+1)k+1e)We must demonstrate that P(k+1) is also true.(k+1)≠(k+1)⋅k!&amp;lt;(k+1)⋅kk&amp;lt;(k+1)⋅(k+1)k=(k+1)k+1=(k+1)k+1&amp;nbsp;P(k+1)&amp;nbsp;is also true.f) Conculusion P(b) is true for all positive integers n greater than 1 according to the mathematical induction principle.

Let P(n) be the statement thatn!<n^nwhere n is an inte

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