How would I go about finding sigma notation for any given set of numbers? I really struggle at finding this. Like is there an easy way to write sigma notation just from looking at a set of numbers? Thanks

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- Nov 12th 2008, 08:17 AMBCHurricane89Sigma Notation from given set of numbers
How would I go about finding sigma notation for any given set of numbers? I really struggle at finding this. Like is there an easy way to write sigma notation just from looking at a set of numbers? Thanks

- Nov 12th 2008, 09:40 AMPlato
- Nov 12th 2008, 09:44 AMBCHurricane89
For example, your given the set of numbers: -2+4-6+8-10

Write the sum in sigma notation.

Id like to know how to figure these type of problems out, as I don't quite understand where to start. - Nov 12th 2008, 09:59 AMPlato
Examine the

**pattern**.

Every term is even and the signs alternate.

Using is a standard way to alternate signs.

There is no easy answer to that question. Experience and lots of practice is the key.

**Pattern recognition**is the most important skill you can have to help you. - Nov 12th 2008, 10:00 AMChris L T521
There are 5 elements, so our sum will have limits from k=1 to 5.

Next step is to try to find a pattern.

We see that the signs alternate, suggesting that there is a term in this sequence. Since the first term is negative, and we're starting from k=1 (which is an odd number), we see that the sequence will include a .

Now, what is the kth term of the sequence ?

We note that this is the sequence of even numbers. and we know that ; this suggests that the kth term is .

We can now see that this sum can be expressed as follows:

Does this make sense?

--Chris

EDIT: Plato beat me. As he mentioned,**pattern recognition**is very important!! - Nov 12th 2008, 10:12 AMBCHurricane89
Ok, i kinda see where your going. Whats the difference, because one of you has , and the other has (-1)^(k+1) is there any difference? I have a test today, and this will be on it, and I was looking at my notes, trying to figure out a way to do these, but this helps.

Oh yeah, also say teh numbers were switched, like 2-4+6-8+10, then it would still be k=1 to 5, then sigma *2k ? - Nov 12th 2008, 10:19 AMChris L T521
- Nov 12th 2008, 10:22 AMBCHurricane89
oh, ok, now I see that