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If a(1), a(2), a(3).... A(n) in R^(+) an...

If `a_(1), a_(2), a_(3).... A_(n) in R^(+) and a_(1).a_(2).a_(3).... A_(n) = 1`, then minimum value of `(1 + a_(1) + a_(1)^(2)) (a + a_(2) + a_(2)^(2)) (1 + a_(3) + a_(3)^(2))..... (1 + a_(n) + a_(n)^(2))` is equal to

A

`3^(n + 1)`

B

`3^(n)`

C

`3^(n - 1)`

D

none of these

Text Solution

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The correct Answer is:
B
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  • If a_(i)gt0 for i u=1, 2, 3, … ,n and a_(1)a_(2)…a_(n)=1, then the minimum value of (1+a_(1))(1+a_(2))…(1+a_(n)) , is

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  • If a_(1), a_(2),…, a_(n +1) are in A.P., then (1)/(a_(1)a_(2)) + (1)/(a_(2)a_(3)) +...+ (1)/(a_(n) a_(n + 1)) is

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    `(n - 1)/(a_(1) a_(n + 1))`
    B
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