smc

We first sum the first $99$ numbers: $\frac{99(100)}{2}=99\cdot 50$. Then, we know that the sum of the series is $99\cdot 50+x$. There are $100$ terms, so we can divide this sum by $100$ and set it equal to $100x$: $$\frac{99\cdot 50+x}{100}=100x\Rightarrow 99\cdot 50=100^{2}x-x\Rightarrow \frac{99\cdot 50}{100^2-1}=x$$ Using difference of squares: $$x=\frac{99\cdot 50}{101\cdot 99}=\frac{50}{101}$$ Thus, the answer is $\boxed{\frac{50}{101}}$.