Cool functions

Algebra Level 5

Let a function \(f(x)\) satisfy :- \(\large f(x) = \dfrac{a^{x}}{a^{x} + \sqrt{a}}\),\((\text{For a>0)}\) and \(\large \displaystyle \sum_{r=0}^{4n} f \bigg(\dfrac{r}{4n+1} \bigg) = \dfrac{1}{1+\sqrt{a}} + 1974\) ,then find the value of \(n\)

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