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Principle of Mathematical Induction — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsPrinciple of Mathematical Induction1 Mark
MCQ
$P(n) = n(n^2– 1)$. Which of the following does not divide $P(k+1)\ ?$
  • A
    $k$
  • B
    $k + 2$
  • ✓
    $k + 3$
  • D
    $k + 1$
✓

Answer

Correct option: C.
$k + 3$
$P(n) = n(n^2- 1)$
$P(k + 1) = (k + 1) ((k + 1)^2-1)$
$P(k + 1) = (k + 1) (k^2+ 1 + 2k - 1)$
$P(k + 1) = (k + 1) (k^2+ 2k)$
$P(k + 1) = (k + 1) k (k + 2)$
Therefore, $k, (k + 1), (k - 1)$ divide $P(k + 1)$.

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