Ok so first question what is the difference between permutations amd combinations? second I don't under stand how to get a working formula for arithmitic, and geometriv series... can someone help me please?

Ok so first question what is the difference between permutations amd combinations? second I don't under stand how to get a working formula for arithmitic, and geometriv series... can someone help me please?
I will only address the first part of your O.P., because I do not understand the second part.
A permutation is:
A combination is:Originally Posted by Wolfram MathWorld
Originally Posted by Wolfram MathWorld
I will illustrate these two concepts with an example:
Suppose I have a box. In this box, there are 4 balls. Each of them is labeled with a number (1 to 4).
A permutation would be a certain rearrangement of the balls in the box. One arrangement could be 1234. Another one could be 1324, or 4213, etc. The number of permutations (or arrangements of the balls in the box) would be ( is in this case the number of balls: 4), thus:
(as there are first four balls to pick from the box, then three, and so on)
A combination is merely picking balls at random from a total of balls in the box, thus:
It should be noted that the balls are not replaced in the box in both cases.
Sources:
Permutation  from Wolfram MathWorld
Combination  from Wolfram MathWorld
Last edited by Cogito Ergo Sum; December 17th, 2013 at 11:05 AM. Reason: Tex commands added.
Ok... So permutation is the number of orders outcomes while a combination (n choose m) just the number of possible out comes of n fitting into m?
Ok now my other question I know the equation for the sum of s=1+2+3+...n1+n is equal to n(n+1) divided by 2 but I don't get how we get the equation. And what if the sequence was 1/2 + 2/2 + 3/2 +... N1/2 + N\2? How do I fin the sum of that by making a formula?
Arithmetic series:
Last edited by KJW; December 17th, 2013 at 12:10 PM.
Geometric series:
Thank you kwj and corito ergo sum.
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