Math CentralQuandaries & Queries


Question from jamelia, a student:

what is this word problem in sigma style i am so lost at this point my first time ever attempting this subject 1+2+3+4+5

Hi Jamelia,

The sigma notation is a shorthand way to represent a sum. The Greek letter Σ somewhat corresponds to the English letter S and for this reason it was chosen to represent a sum.

You have the sum 1 + 2 + 3 + 4 + 5 and I want to introduce a letter i and say 1 + 2 + 3 + 4 + 5 is "the sum of i as i goes from 1 to 5". The shorthand sigma notation for this is

sigma i, i from 1 to 5

The letter Σ stands for sum, what comes after the Σ, in this case i, tells you what to sum and the numbers above and below Σ tell you the range of the summation.

This doesn't seem like much of a shorthand for your example but

sigma i, i from 1 to 100

is much compact than tying to write all 100 term for 1 + 2 + 3 + all the way to 100.

The sigma notation is very useful and versatile. For example if you want the sum of the first 5 positive even integers, 2 + 4 + 6 + 8 + 10 you can write this

sigma 2i, i fro 1 to 5

I read this as the sum of two i as i goes from 1 to 5.

I hope this helps,

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