Sequence And Series Question 381
Question: If $ a_1,a_2…..,a_{n} $ are positive real numbers whose product is a fixed number c, then the minimum value of $ a_1+a_2+…..+{a_{n-1}}+2a_{n} $ is
Options:
A) $ n{{(2c)}^{1/n}} $
B) $ (n+1){c^{1/n}} $
C) $ 2n{c^{1/n}} $
D) $ (n+1){{(2c)}^{1/n}} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] We have $ (a_1+a_2+….+{a_{n-1}}+2a_{n})/n\ge {{(a_1a_2….{a_{n-1}}2a_{n})}^{1/n}} $
$ \Rightarrow ,a_1+a_2+a_3+……+{a_{n-1}}+2a_{n}\ge n{{(2c)}^{1/n}} $
BETA
