# Such Years, Such Summations, Much Wow

Algebra Level 5

Consider a sequence of 2016 real numbers $$a_1,a_2,a_3,\dots,a_{2016}$$ satisfying the property of $$1\leq i \leq 2015$$: $$a_i=\displaystyle\sum_{j=i+1}^{2016} a_j$$.

If $$\displaystyle\sum_{i=0}^{2014} \big((2016-i)a_{i+1}\big)=2015$$, we can express $$\displaystyle\sum_{i=1}^{2016} \dfrac{1}{a_i}$$ as $$a^b\times c -a$$ for positive integers $$a , b$$ and $$c$$, compute $$a+b+c-1$$.

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