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If `a_1, a_2,...... ,a_n >0,` then prove that `(a_1)/(a_2)+(a_2)/(a_3)+(a_3)/(a_4)+.....+(a_(n-1))/(a_n)+(a_n)/(a_1)> n`

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Since `A.M gt G.M`., we have
`(1)/(n) ((a_1)/(a_2)+(a_2)/(a_3)+(a_3)/(a_4)+.....+(a_n-1)/(a_n)+(a_n)/(a_1))((a_1)/(a_2)(a_2)/(a_3)(a_3)/(a_4)....(a_(n-1)a_n)/(a_na_1))^(1//n)`
or `((a_1)/(a_2)+(a_2)/(a_3)+(a_3)/(a_4)+.....(a_(n-1))/(a_n)+(a_n)/(a_1)) gt n(1)^n`
or `((a_1)/(a_2)+(a_2)/(a_3)+(a_3)/(a_4)+....+(a_(n-1))/(a_n))gt n`
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