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Hi,
I'm jwithnell's husband -- I'm a math teacher, and the ti-83 has a couple of functions that will allow you to do what you are asking.
The first is seq() and the other is sum(). You get to both through the 2nd LIST button: seq() through 2nd LIST OPS, sum through 2nd LIST MATH.
The seq function takes an expression, then a variable to increment, the start value, the end value and then an optional step size. What it generates is a list of values of the expression. So seq(x^2, x, 1, 100, 1) would generate the values 1, 4, 9, 16, ... 10000.
The second function, sum(), will then add the values in a list, so it becomes very easy to do the sigma through the two functions.
sum(seq(x^2,x,1,100))
which will then produce the final answer you want 338350. Of course for that particular series, there is a formula ... but I leave that as an exercise for the student! (hint: it is a cubic function)
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