Question

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:

• A. n $\ge$ 1
• B. n $\ge$ 2
• C. n $\ge$ 3
• D. none of these

Answer 1

Answer: (D)

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