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PRINCIPLE OF MATHEMATICAL INDUCTION — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSPRINCIPLE OF MATHEMATICAL INDUCTION1 Mark
MCQ
Let $\mathrm{P}(\mathrm{n}):$ " $2^{\mathrm{n}}<(1 \times 2 \times 3 \times \ldots \times n)$". Then the smallest positive integer for which $\mathrm{P}(\mathrm{n})$ is true is:
  • A
    1
  • B
    2
  • C
    3
  • ✓
    4
✓

Answer

Correct option: D.
4
  1. 4
Solution:
$\mathrm{P}(1)$ : $2^1<1$
$2<1$ is false
$\mathrm{P}(2)$ : $2^2<1 \times 2$
$4<2$ is false
$\mathrm{P}(3): 2^3<1 \times 2 \times 3$
$8<6$ is false
$\mathrm{P}(4): 2^4<1 \times 2 \times 3 \times 4$
$16<24$ is true

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