Isn't \(100000\) such a huge number (Part 4) ?

Algebra Level 5

Let there be a function \(f(x)\) satisfying the relation:

\[f(x)=\dfrac{100000^{x}}{100000^{x}+100\sqrt{10}}.\]

Find \[1 + \displaystyle\sum_{k=1}^{99998}f(\dfrac{k}{99999}).\]

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