13.2 Series and series notation

Begin by defining a series: it’s like a sequence, but with plusses instead of commas. So our phone number example of a sequence, “8,6,7,5,3,0,9” becomes the series “ $8+6+7+5+3+0+9$ ” which is 38.

Many of the other words stay the same. The first term is $t_1$ , the $n^{\mathrm{th}}$ term is $t_n$ , and so on. If you add up all the terms of an arithmetic sequence, that’s called an arithmetic series; and similarly for geometric.

The hardest part about this introduction is the notation. Explain about series notation, using weird examples like $\sum _{n=3}^7\frac{n^2-2}{5}$ just to make the point that even when the function looks complicated, it is not hard to write out the terms .

Note that the “counter” always goes by ones. Does this mean you can’t have a series that goes up by 2s? Ask them how to use series notation for the series $10+12+14+16$ .

Homework: