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I'm looking for a number series I can use for gradually rising or falling numbers. The number series should not be linear and should converge to a number at some point.

$\sqrt[N]{N}$ where $N > 3$; $N \in \mathbb{Z}$. (This series gradually falls)

Its inverse is then used for the opposite

I've verified for $N$ for the set $[4,5,\ldots,9]$

Do you know about other options? Other things I should consider?

They don't need to be inverses.

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    Ill graph it to see what it looks like. I'm interested is as many options as possible and they don't need to be inverses. Thanks for the help.2012-10-25

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You can use $e^{-kn}$ for a falling series and $1-e^{-kn}$ for rising. Or $\frac 1{1+n}$ for falling and $\frac n{n+1}$ for rising. There are lots of possibilities-better definition is needed.

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    i ended up deciding to use something similar to this http://gamedev.stackexchange.com/questions/20934/how-to-create-adjustable-formula-for-rpg-level-up-requirements2012-10-26