Inequality with summation

If ${a}_{i}$ positive numbers and $n\ge 2$ (the subscripts are taken modulo $n$), how can I prove the following inequality

$n\sum _{k=1}^{n}\frac{1}{(n-1){a}_{k}+{a}_{k+1}}\le \sum _{k=1}^{n}\frac{1}{{a}_{k}}$?

If ${a}_{i}$ positive numbers and $n\ge 2$ (the subscripts are taken modulo $n$), how can I prove the following inequality

$n\sum _{k=1}^{n}\frac{1}{(n-1){a}_{k}+{a}_{k+1}}\le \sum _{k=1}^{n}\frac{1}{{a}_{k}}$?