A) \[n+\frac{1}{n}\]
B) \[n-\frac{1}{n}\]
C) \[2n+\frac{1}{n}\]
D) never less than n
Correct Answer: D
Solution :
Let \[{{x}_{1}},{{x}_{2}},.....{{x}_{n}}\] are n positive integers. \[\because \] \[AM\ge GM\] \[\therefore \] \[\frac{{{x}_{1}}+{{x}_{2}}+....+{{x}_{n}}}{n}\ge {{({{x}_{1}}.{{x}_{2}}....{{x}_{n}})}^{1/n}}\] \[\Rightarrow \] \[\frac{{{x}_{1}}+{{x}_{2}}+....+{{x}_{n}}}{n}\ge \,\,{{(1)}^{1/n}}\] \[\Rightarrow \] \[{{x}_{1}}+{{x}_{2}}+...+{{x}_{n}}\ge n\] Hence, their sun is never lea than n.
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