It turns out that if we've got a geometric series, then S of T is equal to T0,

which is the initial amount or principle financial language times and

then that's 1 minus theta to the power T plus 1 over 1 minus theta.

And so now you can see why you need to know about these

power functions if you're going to become useful in this quantitative modeling.

You certainly need a certain set of mathematical skills, and I did

present the functions that I think you you absolutely need to feel comfortable with.

So, here's the panel function coming in.

Now with a formula like this,

I don't have to go through the process of working out each individual year's catch.

I can just plug straight in to the formula.

And if I do that for this particular geometric series where P0 is equal to

200,000 and theta was equal to .95,

T I'm summing up to, in the fisheries example year five, so T is equal to 5,

I have to put in 5 plus 1 and I get exactly the same number out as I got

before, 1,059,632.

So it's encouraging that it's the same.

It has to be the same.

But what you can see here is that one of the advantages of

a quantitative model is it can potentially provide a much more efficient

way of doing calculations than if you looked at things

on a time by time period in the spreadsheet type world view.

Where yes, you can do this in a spreadsheet and add it up.

But imagine we have a situation where we wanted to go out a time period that was

more rows than you could put in a spreadsheet.

Your spreadsheet approach just wouldn't work anymore, but

you've always got the formula to use.

And so there are situations where taking the time to

formalize the business process through a quantitative model will give you much more

efficient ways of computation than through a spreadsheet.

So I'm not knocking spreadsheets.

I'm not saying there's no use for them.

But I'm saying that there are certain sorts of problems that can be very

efficiently solved through the formulae that we're able to generate

through having taken the time to create a quantitative model.

And here's an example of such a formula.

So the sum of a geometric series.