Question 10
Let $a$, $b$, $c$, $d$ and $e$ be positive real numbers. Determine the largest value that the following expression can take:
$$
\frac{a b+b c+c d+d e}{2 a^{2}+b^{2}+2 c^{2}+d^{2}+2 e^{2}}
$$
$$
\frac{a b+b c+c d+d e}{2 a^{2}+b^{2}+2 c^{2}+d^{2}+2 e^{2}}
$$