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Question

# Let P(n) be the statement 2n<n! where n is a natural number, then P(n) is true for:

A
all n
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B
all n>2
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C
all n>3
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D
all n<3
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Solution

## The correct option is C all n>3We have, P(n) be the statement 2n<n! Where n is a natural number Then, Put n=1,2,3.... So, P(1) be the statement of 21<1!=2<1(Itiswrong) P(2) be the statement of 22<2!=4<2(Itiswrong)P(3) be the statement of 23<3!=8<6(Itiswrong)But,P(4) be the statement of 24<4!=16<24(Itisright) Similarly, P(5),P(6)....... So, all number n is a natural number.Therefore, it is true for all n>3.Hence, this is the answer.

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