sum _(i=1)^10000i=1+2+3+ldots +10000 50005000 50500000 50050005 50005005 infty

## Step 1: Identify the Upper Limit of Summation<br />### The given series is $\sum_{i=1}^{10000} i$. The upper limit of summation is 10000. Since the upper limit is a finite number, the series is finite.<br /><br />## Step 2: Calculate the Sum<br />### This is an arithmetic series with $n = 10000$, $a_1 = 1$, and $a_n = 10000$. The sum of an arithmetic series is given by $S_n = \frac{n(a_1 + a_n)}{2}$. Substituting the values, we get $S_{10000} = \frac{10000(1 + 10000)}{2} = \frac{10000(10001)}{2} = 5000(10001) = 50005000$.