A) \[n{{(2C)}^{1/n}}\]
B) \[\left( n+1 \right){{c}^{1/n}}\]
C) \[2n{{c}^{1/n}}\]
D) \[(n+1){{\left( 2c \right)}^{1/n}}\]
Correct Answer: A
Solution :
[a] \[A\ge G\] \[\frac{{{a}_{1}}+{{a}_{2}}+{{a}_{3}}+.....+{{a}_{n-1}}+2{{a}_{n}}}{n}\] \[\ge \sqrt[n]{{{a}_{1}}.{{a}_{2}}.{{a}_{3}}.....{{a}_{n-1}}2{{a}_{n}}}\] \[{{a}_{1}}+{{a}_{2}}+....+{{a}_{n-1}}+2{{a}_{n}}\ge n.{{\left( 2c \right)}^{1/n}}\]
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