Sigma notation: What exactly is i?

[giant016]

I've kind of got this approximating the area of a plane region down, but I don't know what i really is. The book calls it the "index of summation", which might as well be a foreign language.

On a similar note, what is c sub i?

Thanks.

 

[chroot]

If you're summing up ten things, you could label each one with a number from one to ten. Conventionally, this label would be drawn as a subscript. If you had ten apples, each represented by the letter a, then each individual apple would be labeled a₁ to a₁₀.

If you were to add up something about them -- say, their weight -- you would have a sum that runs from 1 to 10. If the weight of an apple is represented by w(a_i), then the sum would look like:

$\sum\limits_{i = 1}^{10} {w\left( {a_i } \right)}$

In english, this would be spoken "the sum of the weight of apples a-one through a-ten." The "index of summation" is the variable that is being changed; in this case, it's i.

- Warren

 

[mathwonk]

i is nothing. it could also be r or q or j or anything else. it is like a preposition "it", which emans nothing unlkess you know the antecedent.

it is just sued as a pplace holder for something else, that is why an innocuous lookingn letter with no emaning of its own is chosen.

in warren's example, "i" variously holds the place of the numbers 1,2,3,4,...,10.its like asking what "he" means in the sentence "If anyone in the class needs help, I'm going to see he gets it."

just as "he" refers back to anyone who needs help, so "i" refers back to the numbers 1,...10.