In fact pa is true for all integers n greater than a particular base value and you should complete the proof given below to use the principle of mathematical induction to prove this.(adsbygoogle = window.adsbygoogle || []).push({});

pa : n-2 < (n^2 – 3n)/12

Base case is n = 14

Because: n-2 < (n^2 – 3n)/12

14-2 < (196-42)/12

12 < 154/12

12 < 12.83

Inductive step

Inductive Hypothesis : Assume pa(k) is true for some k > 10. Thus k-2 <(k^2 – 3k)/12.

We must prove that pa(k+1) is true i.e. that (k+1)-2 < ((k+1)^2 – 3(k+1))/12

Now to prove such an inequality we always start with the more complicated side:

((k+1)^2 – 3(k+1))/12 = (k^2 + 2k +1 – 3k – 3)/12

= (k^2 – 3k)/12 + (2k-2)/12

> ....?... + (2k-2)/12 ……(b) because

> ..?............. because

This is the question i have been given to do although no idea on how to to finish it any ideas anyone ?

thanks

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# Induction Hypothesis:

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