To begin our lesson on Riemann Sums, it seems reasonable that we start by adding stuff up. Here, we'll sum the first 10, 100, and n integers using a method Gauss developed when he was a wee lad. Duration: 7:42

Animated story of how Gauss added the first 100 whole numbers to avoid beatings and chalk dust. Duration_12_05

Numberphile uses Gauss's addition trick to add all of the digits (not numbers) from 1 to 1,000,000. Duration_7_03

After discussing the essential parts of a summation, we'll take a look at a variety of sums. Number 4 there seems to be a bit of an outlier. I wonder if it is of any particular significance. Duration: 12:19

When computing a summation, we try to pare it down into simpler parts, like the sum of constants, the sum of integers, the sum of squared integers, and so on, simply because we have formulae for each of those. Sort of like your name, you don't have to have these formulae memorized; you just need to be able to apply them within a given summation. Duration: 7:14

Finally, let's apply the various properties of Summations here in Example 2. When we're done, we'll go ahead and link this lesson back to a former unit by taking the limit of our result, since I have a pretty good feeling it might come up again. Duration: 7:26