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1.3 + 3.5 + 5.7 + ..... + (2n - 1)(2n + 1) = (n(4n^2 + 6n - 1))/3, for all n∈N.

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1.3 + 3.5 + 5.7 + ..... + (2n - 1)(2n + 1) = (n(4n2 + 6n - 1))/3, for all n∈N.

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which is P(k +1) 

Thus, P(k) ⇒ P(k +1). 

Hence, by mathematical induction P(n) is true for all n∈N

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