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Series and Series Notation

Module by: Kenny M. Felder. E-mail the author

Summary: A teacher's guide to lecturing on 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 8+6+7+5+3+0+9” which is 38.

Many of the other words stay the same. The first term is t 1 t 1 , the n th n th term is t n 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 ∑n=37n2−25∑n=37n2−25 size 12{ Sum cSub { size 8{n=3} } cSup { size 8{7} } { { {n rSup { size 8{2} } - 2} over {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 10+12+14+16.

Homework:

“Homework—Series and Series Notation”

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