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Principle of Mathematical Induction — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsPrinciple of Mathematical Induction1 Mark
MCQ
What will be $P(k + 1)$ for $P(n) = n^3(n + 1)?$
  • A
    $ (k+1)^4$
  • ✓
    $ k^4+5 k^3+9 k^2+7 k+2 $
  • C
    $ k^4+6 k^3+9 k^2+7 k+2 $
  • D
    $k^4+3 k^3+9 k^2+6 k+2 $
✓

Answer

Correct option: B.
$ k^4+5 k^3+9 k^2+7 k+2 $
$P(n)=n^3(n+1)$
$P(k+1)=(k+1)^3(k+1+1)$
$P(k+1)=\left(k^3+3 k^2+3 k+1\right)(k+2)$
$P(k+1)=k^4+3 k^3+3 k^2+k+2 k^3+6 k^2+6 k+2$
$P(k+1)=k^4+5 k^3+9 k^2+7 k+2$

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