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  4. If P(n): 2 + 4 + 6 +... + (2n), n ∈ N, then P(k) = k (k + 1) + 2 implies P (k + 1) = (k + 1) (k + 2) + 2 is true for all k ∈ N. So statement P(n) = n (n + 1) + 2 is true for:

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Q. If P(n) : 2 + 4 + 6 +... + (2n), n $\in$ N, then P(k) = k (k + 1) + 2 implies P (k + 1) = (k + 1) (k + 2) + 2 is true for all k $\in$ N.
So statement P(n) = n (n + 1) + 2 is true for:

Principle of Mathematical Induction

Solution:

P(1) = 2 and k(k + 1) + 2 = 4, So P(1) is not true. Mathematical Induction is not applicable.