# Come on, the information is not at all sufficient!

Algebra Level 5

Consider $$k$$ positive real numbers: $$a_1,a_2,a_3,\ldots , a_{k}$$ such that $$\displaystyle\prod_{i=1}^{k} a_i=2016$$ and $$\displaystyle\sum_{i=1}^{k} a_i^{k}=2016 k$$ for some positive integer $$k$$.

Then, find the value of $$\displaystyle\sum_{i=1}^{2014} \dfrac{a_i}{a_{i+1}+a_{i+2}}$$.

×