If `a_(1)gt0` for all `i=1,2,…..,n`. Then, the least value of `(a_(1)+a_(2)+……+a_(n))((1)/(a_(1))+(1)/(a_(2))+…+(1)/(a_(n)))`, is
A
`n^(2)`
B
2n
C
n
D
`(1)/(n)`
Text Solution
Verified by Experts
The correct Answer is:
B
Using `A.M.geG.M.,` we have `(a_(1)+a_(2)+...+a_(n))/(n)ge(a_(1)a_(2)...a_(n))^(1//n)" "...(i)` `implies(a_(1)+a_(2)+...+a_(n))gen(a_(1)a_(2)...a_(n))^(1//n)` Again, using `A.M.geG.M.,` we have `((1)/(a_(1))+(1)/(a_(2))+...+(1)/(a_(n)))/(n)ge((1)/(a_(1))xx(1)/(a_(2))xx...xx(1)/(a_(n)))^(1//n)` `implies((1)/(a_(1))+(1)/(a_(2))+...+(1)/(a_(n)))gen((1)/(a_(1)a_(2)......a_(n)))^(1//n)" "...(ii)` From (i) and (ii), we get `(a_(1)+a_(2)+...+a_(n))((1)/(a_(1))+(1)/(a_(2))+...+(1)/(a_(n)))` `gen|a_(1)a_(2)......a_(n)|^(1//n)xx{(n)/((a_(1)a_(2)....a_(n)))}^(1//n)` `implies(a_(1)+a_(2)+....+a_(n))((1)/(a_(1))+(1)/(a_(2))+....+(1)/(a_(n)))gen^(2)`
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OBJECTIVE RD SHARMA-INEQUALITIES -Section II - Assertion Reason Type
