Dividing a Number into Unequal Parts

[serdar]

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?

[JosAH]

@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

[serdar]

Hmm, you explained it so clear -and fast. Thanks very much.

I think I need a 'simple maths' sub-forum here to post :)

[r035198x]

Ha, the off-by-one does Jos in again.