# An over-ambitious AP

Algebra Level 4

Let $${a_{i}},0 \le i \le n$$ be an arithmetic progression (AP) such that $$a_{0} = 16$$ and $$a_{j} > 0$$ for all $$j \ge 0$$.

Also,every three consecutive terms of this AP satisfy the inequality $\displaystyle \dfrac{1}{a_{n}} \ge \dfrac{1}{\sqrt{a_{n+1} \cdot a_{n-1}}}.$

Find the value of $$\displaystyle \sum_{j=0}^{99} \dfrac{\sqrt[4]{a_{j}}}{a_{j}}$$.

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