let $n \ge3 $ be an arbitrarily fixed integer. Take all the possible finite sequences $(a_1,\ldots,a_n)$ of positive numbers. Find the least upper and the greatest lower bounds of the set of real numbers
$\sum_ {k=1}^{n} \frac{a_k}{a_{k } + a_{k+1} +a_{k+2}}$ where put $a_{n+1} =a_1 $and $a_{n+2} =a_2$
my ideas: I take $ a_k = x^k$ where $k>0$. Then $\sum_{k=1}^{n} \frac{a_k}{a_{k } + a_{k+1} +a_{k+2}}=$ $\frac {x}{x+x^2+x^3} +\cdots + \frac{x^{n-2}} {x^{n-2} +x^{n-1} +x^n} +\cdots +\frac{x^n}{x^n+x+x^2}$,
here I don't know how to proceed further.
Anybody please help me....I would be more thankful
Thanks in advance