If P(k) = k^2 (k + 3) (k^2 – 1) is true, then what is P(k + 1)?(a) (k + 1)^2 (k + 3) (k^2 – 1)(b) (k + 1)^2 (k + 4) (k^2 – 1)(c) (k + 1)^2 (k + 4) k (k + 2)(d) (k + 1) (k + 4) k (k +2)I had been asked this question in unit test.Asked question is from The Principle of Mathematical Induction in portion Principle of Mathematical Induction of Mathematics – Class 11

If P(k) = k^2 (k + 3) (k^2 – 1) is true, then what is P(k + 1)?(a) (

1.	If P(k) = k^2 (k + 3) (k^2 – 1) is true, then what is P(k + 1)?(a) (k + 1)^2 (k + 3) (k^2 – 1)(b) (k + 1)^2 (k + 4) (k^2 – 1)(c) (k + 1)^2 (k + 4) k (k + 2)(d) (k + 1) (k + 4) k (k +2)I had been asked this question in unit test.Asked question is from The Principle of Mathematical Induction in portion Principle of Mathematical Induction of Mathematics – Class 11
Answer» CORRECT choice is (c) (K + 1)^2 (k + 4) k (k + 2) Easiest explanation: In mathematical induction, if P(k) is true, we need to prove that P(k + 1) is also true. Here P(k + 1) is FOUND by substituting (k + 1) in place of k. P(k + 1) = (k + 1)^2 (k + 1 + 3) ((k + 1)^2 – 1) P(k + 1) = (k + 1)^2 (k + 4) (k^2 + 1 + 2k – 1) P(k + 1) = (k + 1)^2 (k + 4) (k^2 + 2k) P(k + 1) = (k + 1)^2 (k + 4) k (k +2)

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