SATHEE: Principle Of Mathematical Induction Question 32

Principle Of Mathematical Induction Question 32

Question: Let $ P(n):‘‘2^{n}<(1\times 2\times 3\times …\times n)’’. $ Then the smallest positive integer for which P(n) is true is

Options:

A) 1

B) 2

C) 3

D) 4

Show Answer

Answer:

Correct Answer: D

Solution:

[d] Since $ P(1):2<1 $ is false; $ P(2):2^{2}<1\times 2 $ is false $ P(3):2^{3}<1\times 2\times 3 $ is false; $ P(4):2^{4}<1\times 2\times 3\times 4 $ is true

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Principle Of Mathematical Induction Question 32

Question: Let $ P(n):‘‘2^{n}<(1\times 2\times 3\times …\times n)’’. $ Then the smallest positive integer for which P(n) is true is

Options:

Answer:

Solution:

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