disregardthat

Science Advisor

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## Main Question or Discussion Point

*(This is not a homework question!)*

I have no education in this kind of math yet, but I wonder how many ways you are allowed to use the summation sign sigma. I can't seem to get a good explanation on google or wikipedia.

Since I like to try myself with tex, I will write an example of it here:

[tex]\sum_{k=3}^4 k^2[/tex] This will be a normal summation sign.

To see if I have got it right: [tex]k = 3[/tex] means that the k on the side of the sigma will start at 3, right?

If the sigma is raised to 4 like the one I have shown, it means that the k (3) will be added to a number 3+1, and then to 4+1, and then to 5+1. That the k is raised to the power of two, means that for each part of the serie, the number will be raised, like (3)^2 + (3+1)^2 + (4+1)^2... right?

I think this will be the same as: [tex]\sum_{k=3}^4 k^2 = 3^2 + 4^2 + 5^2 + 6^2 = 86[/tex]

Is this the correct use of the Summation?

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I have heard that it is used in biology to find out the number of cells that is being reproduced.

Let's say that we have a cell, and it has unlimited food, so it will reproduce in the rate of doubling each ten minutes. And we will watch it for one minute. That means that the cell and it's daughter cells will reproduce 60\10 = 6 times.

I found out that the only way that can be done is if you put it up like this:

[tex]\sum_{k=0}^6 2^k[/tex]

So I guess it would give us the right answer of how many cells that would be there.

[tex]\sum_{k=0}^6 2^k = 2^0 + 2^1 + 2^3 + 2^4 + 2^5 + 2^6 = 127[/tex]

The amount of cells that we will end up with, assuming none of them died, and assuming every cell reproduced itself each ten minutes, after one minute.

**Is**this a valid way of using the summation? If not, it should be

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