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Statement-1 : If a1,a2,a3,….. an are pos...

Statement-1 : If `a_1,a_2,a_3`,….. `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 `n(2C)^(1/n)`
Statement-2 :A.M. `ge` G.M.

A

`n(2c)^(1//n)`

B

`(n+1)c^(1//n)`

C

`2nc^(1//n)`

D

`(n+1)(2c)^(1//n)`

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Knowledge Check

  • If a_1,a_2 …. a_n are positive real numbers whose product is a fixed real number c, then the minimum value of 1+a_1 +a_2 +….. + a_(n-1) + a_n is :

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

  • If a_i > 0 for i=1,2,…., n and a_1 a_2 … a_(n=1) , then minimum value of (1+a_1) (1+a_2) ….. (1+a_n) is :

    A
    `2^(n//2)`
    B
    `2^n`
    C
    `2^(2n)`
    D
    `1`

  • If a_1,a_2,a_3,…….a_n are in Arithmetic Progression, whose common difference is an integer such that a_1=1,a_n=300 and n in[15,50] then (S_(n-4),a_(n-4)) is

    A
    `(2491,247)`
    B
    `(2490,248)`
    C
    `(2590,249)`
    D
    `(248,2490)`

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