Geometric progression formula confusion with 100(1.01)(1.01n-1/1.01-1)

[radnorgardens]

Morning/afternoon/evening all,

I'm aware of the formula: a(rⁿ-1/r-1).

However, for the following:

100(1.01)(1.01ⁿ-1/1.01-1)

Apparently (Mathematics for Economics and Business - Ian Jacques), this is the same as:

10,100(1.01ⁿ-1)

Is that correct? I can't find out how to get to this.

Your help is always appreciated.

 

[Dr.Peterson]

Morning/afternoon/evening all,

I'm aware of the formula: a(rⁿ-1)/(r-1).

However, for the following:

100(1.01)(1.01ⁿ-1)/(1.01-1)

Apparently (Mathematics for Economics and Business - Ian Jacques), this is the same as:

10,100(1.01ⁿ-1)

Is that correct? I can't find out how to get to this.

Your help is always appreciated.

I added parentheses that are needed to make this mean what you intended.

Here is how you get the simplified form:

100(1.01)(1.01ⁿ-1)/(1.01-1) = 101 (1.01ⁿ-1)/(0.01) = 101/0.01 (1.01ⁿ-1) = 10100 (1.01ⁿ-1)

Follow that? (100)(1.01) = 101, and dividing by 0.01 multiplies by 100.

 

[radnorgardens]

I added parentheses that are needed to make this mean what you intended.

Here is how you get the simplified form:

100(1.01)(1.01ⁿ-1)/(1.01-1) = 101 (1.01ⁿ-1)/(0.01) = 101/0.01 (1.01ⁿ-1) = 10100 (1.01ⁿ-1)

Follow that? (100)(1.01) = 101, and dividing by 0.01 multiplies by 100.

Ah right. Because when I expand it out:
101 x (1.01ⁿ-1) / 0.01

Then rearrange to:
101 / 0.01 x (1.01ⁿ-1)

Becomes:
10100 x (1.01ⁿ-1) i.e. 10100 (1.01ⁿ-1)

Great - thank you Dr.Peterson.