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Dividing a Number into Unequal Parts

88
Title looks unclear but what I need is fairly simple:

Suppose we have a rope 100cm long, and we want to divide it into 10 equal parts. In this case each part would be 10cm long.

Now, what if we want to divide it into unequal parts; say each part will be x times longer than the previous part. How to write such an equation?
Dec 16 '08 #1
3 9715
JosAH
11,448 Expert 8TB
@serdar
If the smallest piece of rope has length l (lower case ell) then the next parts have lengths x*l x^2*l x^3*l ... x^9*l (ten pieces in total).

The sum of these numbers must equal 100 so:

l+x*l+x^2*l+ ... x^9*l == 100 -->

l*((1-x^10)/(1-x)) == 100 -->

x is a constant so:

l*C == 100 --> l == 100/C

kind regards,

Jos
Dec 16 '08 #2
serdar
88
Hmm, you explained it so clear -and fast. Thanks very much.

I think I need a 'simple maths' sub-forum here to post :)
Dec 16 '08 #3
r035198x
13,262 8TB
Ha, the off-by-one does Jos in again.
Dec 17 '08 #4

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