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Question

# Assertion :STATEMENT-1 : 1.3.5.....(2n−1)>nn,nϵN Reason: STATEMENT-2 : The sum of the first n odd natural numbers is equal to n2

A
Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
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B
Statement-1 is True, Statement-2 is True; Statement-2 is Not a correct explanation for Statement-1
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C
Statement-1 is True, Statement-2 is False
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D
Statement-1 is False, Statement-2 is True
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Solution

## The correct option is D Statement-1 is False, Statement-2 is True1+3+5+...+(2n−1)=n2(2+(n−1)2)=n2∴ Statement 2 is true.Now, applying AM≥GM to the n odd numbers 1+3+...+(2n−1)n≥(1.3.5...(2n−1))1n⇒n2n≥(1.3.5...(2n−1))1nor (1.3.5...(2n−1))≤nnThus Statement 1 is False

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