Question-71

Question-71

Use mathematical induction to prove that 3 divides n^{3} + 2 n whenever n is a positive integer.

 

solution

 

The statement is true for the base case, n = 1 , since 3 \mid (1^{3} + 2.1). Suppose that 3 \mid (k^{3} + 2k). We must show

that 3 \mid ((k +1)^{3} + 2(k + 1)) . If we expand the expression in question, we obtain (k^{3} + 2 k) + 3 (k^{2} + k +1 ) . By

the inductive

 

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