Calculating Number of Folders: 4^4 + 4^3 + 4^2 + 4^1

[WarrickF]

Hi All,

Quick disclaimer – I'm no math genius ;)

I have written a quick script that take as it's input the number of levels you'd like to iterate and the number of folders at each level you'd like to create.

So you have 4 base folders, in each folder you have 4 more folders etc. 4 levels deep.

The math to calculate how many folders there are at the end of the day looks something like this:

4^4 + 4^3 + 4^2 + 4^1

I can do this math manually, but I have no idea how to create a formula that allows me to plug in any number. Let's say I wanted to go 12 levels deep .. how many folders would I end up with? I can do this manually of course, but then I would learn nothing and run into the same problem a yeaqr from now when I need to do the same math with 1000 folders ;)

I'm trying to do this in Excel \ Open Office so any formula references you can give would also be greatly appreciated.

Thanks
Warrick

 

[shmoe]

it's a geometric series:

$$\sum_{i=0}^{n}r^i=\frac{1-r^{n+1}}{1-r}$$

(r not equal to 1)

 

[Architeuthis Dux]

Hello Warrick,

Thank you for sharing your script and question with us. I can provide some insights into the mathematical expression you have provided.

The expression 4^4 + 4^3 + 4^2 + 4^1 represents a geometric series, where the sum of each term is calculated by multiplying the previous term by a constant factor (in this case, 4). This type of series can be represented by the formula Sn = a(r^n - 1)/(r-1), where Sn is the sum of the first n terms, a is the first term, and r is the common ratio.

In your case, a = 4 (the first term), r = 4 (the common ratio), and n = 4 (the number of terms). Plugging these values into the formula, we get:

Sn = 4(4^4 - 1)/(4-1) = 4(256-1)/3 = 4(255)/3 = 1020/3 = 340

So, for 4 levels, the total number of folders would be 340.

If you wanted to extend this expression to 12 levels, you can simply plug in n = 12 and use the same formula. This would give you a total of 4,194,304 folders at the end.

In terms of creating a formula in Excel or Open Office, you can use the POWER function (represented by ^) to raise a number to a certain power. So, for example, the formula for 4 levels would be =4^4 + 4^3 + 4^2 + 4^1. To make this formula dynamic, you can replace the numbers with cell references, for example, =A1^A1 + A2^A2 + A3^A3 + A4^A4, where A1 is the number of levels and A2, A3, and A4 represent the number of folders at each level.

I hope this helps and good luck with your project!

Best,