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Prove the following by using the principle of mathematical induction for all n ∈ N:
1.  41n – 14n is a multiple of 27.
2.  (2n + 7) < (n + 3)2.

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1.  41n – 14n is a multiple of 27. 

2.  (2n + 7) < (n + 3)2.

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