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

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

Now, $f(1-x)=\dfrac{100000^{1-x}}{100000^{1-x}+100\sqrt{10}}$ which is equal to $\dfrac{100\sqrt{10}}{100000^{x}+100\sqrt{10}}$ .

Now, on keen and vigil observation, we see that:

$f(x)+f(1-x)=1$ .

So, $f(\dfrac{1}{99999})+f(\dfrac{99998}{99999})=1$

$f(\dfrac{2}{99999})+f(\dfrac{99997}{99999})=1$

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and so there would be $49999$ such pairs of sum whose each sum is $1$ .

So, our answer is $49999\times 1=49999$ .

Adding $1$ to it, our final answer becomes $\huge {50000}$ which is definitely huge!