Ok I Have A Neat Math Thing For Ya... I invented it myself :)

[zanzibarjones 1]

Ok here it goes:Take any 5 consecutive numbers and write them down vertically on a sheet of paper.i.e.:12345Now going down the line, square these guys and write the answer to the left:1*1=12*2=43*3=94*4=165*5= 25Now, going down the line again, take the smaller total and subtract it from the total below it, and write it between the 2 to the right, like so:1 >34 >59 >716 >925And do it one more time with those answers: and you will always come up with the answer 2.I am not sure why this happens, but here is the next cool part (Don't ask me why I thought of this in the shower, I have no idea why)Take another set of numbers, they have to be consecutive and cube them and do the same process, the answer will always come out as 6. (You may have to increase the number of consecutive numbers, in order to subtract all the way out to the common answer)Ready for the next cool part, want the answer to if you did those consecutive number to the power of 4? The answer will always be 24. Want to know how I know that? All you have to do, is take the subtraction answer of set 1 and multiply it times the power of the next set.So like this:Set 1, the set you multiplied by a power of 2, it's answer is 2Set 2, the set you multiplied by a power of 3, it's answer is 6 (2*3)Set 3, the set you multiplied by a power of 4, it's answer is 24 (6*4)Set 4, the set you would multiply times a power of 5, it's answer will be 120 (24*5)And then after doing a bunch of those, and subtracting all those answer out, somewhere down the line it all comes back to 1,2,3,4,5,6,...etc. Weird huh?Explain that one for me. Or if you need me to, I'll do it on paper and scan it in, if it's confusing to you guys and gals.

Edited August 30, 2010 by zanzibarjones (see edit history)

[Bikerman 2]

The first thing to do is see if you can tell what any term is going to be in advance.

For that you need to generalise the pattern into algebra.

You have already put it into words so it is easy. Any term is equal to the previous term multiplied by the current term.

In algebra that is a_n = a(n-1)*n

This is known as a geometric sequence.

I'm not going to spoil it by going further - the whole point of maths is to play with the patterns and see what deeper 'truths' you can find...

 

* Just as a spur, think about the numbers 1,2,6,24,120 a bit more, and look at the algebra. These numbers are called 'factorials' which can be expressed another way {1*2*3* ... *n}