Might Wanna Use A Calculator

$\begin{aligned} h(n) & = \frac {\bigg(\frac {\left(\frac {n^2}n \right)^{200}}{n^{199}}\bigg)^{1000000}}{n^{999998}} = \frac {\left(\frac {n^{200}}{n^{199}}\right)^{1000000}}{n^{999998}} = \frac {n^{1000000}}{n^{999998}} = n^2 \end{aligned}$

Therefore, $\displaystyle \sum_{n=1}^{100} h(n) = \sum_{n=1}^{100} n^2 = \dfrac {100(101)(201)}6 = \boxed{338350}$ .

First, we need to simplify that seemingly huge fraction in the function. We notice a pattern, so when we simplify it down, we get $n^2$ . Basically, the problem is asking us to find the sum of all terms up until $100$ in the function $h(x)=n^2$ . We can create an equation to model this problem:

$\displaystyle \sum_{k=1}^{100}n^2=1^2+2^2+3^2+4^2+5^2+\dots+100^2=\boxed{338350}$