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how do you prove this proposition using mathematical weak induction? 9n+14 <= 23n^2 please show your...

how do you prove this proposition using mathematical weak induction? 9n+14 <= 23n^2

please show your work and explain it.

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Answer #1

We have the hypothesis :

Base Case :

For k = 1, we have

LHS

RHS

Thus, LHS <= RHS.

Thus, our hypothesis holds true for base case, k = 1.

Assumed Case :

We assume that out hypothesis holds true for k + 1.

That is,

Inductive Case :

For k + 1, we have

LHS

From our assumed case, we continue as

Also, since k is a positive integer, we further continue as

Thus, LHS <= RHS

Hence, proved via weak-induction.

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