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 `a_(n-1)+2a_n` is b. `(n+1)c^(1//n)` `2n c^(1//n)` `(n+1)(2c)^(1//n)`

Options

A. `n(2c)^(1//n)`
B. `(n+ 1)c^(1//n)`
C. `2nc^(1//n)`
D. `(n+ 1) (2c)^(1//n)`

Answer

A

Explanation

`A ge G`
`(a_(1) + a_(2) + a_(3)+ ..... + a_(n-1) + 2a_(n))/(n) ge root(n)(a_(1).a_(2).a_(3)"....."a_(n-1)2a_(n))`
`a_(1) + a_(2) +"……" + a_(n-1) + 2a_(n) ge n.(2c)^(1//n)`