Sequence And Series Question 317
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
[IIT Screening 2002]
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.M. $ \ge $ G.M. Þ $ \frac{a_1+a_2+….+{a_{n-1}}+2a_{n}}{n}\ge {{(a_1.{a_{2,}}…{a_{n-1}}2a_{n})}^{\frac{1}{n}}}\ge {{(2c)}^{\frac{1}{n}}} $ \ Minimum value of
BETA
