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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