A) \[{{\left( 1+\frac{1}{n} \right)}^{n}}<{{n}^{2}},n\] is a positive integer
B) \[{{\left( 1+\frac{1}{n} \right)}^{n}}<2,n\] is a positive integer
C) \[{{\left( 1+\frac{1}{n} \right)}^{n}}<{{n}^{3}},n\] is a positive integer
D) \[{{\left( 1+\frac{1}{n} \right)}^{n}}>2,n\] is a positive integer
Correct Answer: D
Solution :
[d] Put \[n=1,{{\left( 1+\frac{1}{1} \right)}^{1}}=2\] \[\therefore {{\left( 1+\frac{1}{n} \right)}^{n}}>2,\] n is a positive integer.
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