Given the formula for present value of future cash flows...

$P{V}_0=C{F}_0+\frac{C{F}_1}{(1+r{)}^1}+\frac{C{F}_2}{(1+r{)}^2}+$dots$+\frac{C{F}_t}{(1+r{)}^2}$

Show how you get from the above formula dealing with a finite

amount of cash flows to the formula for a perpetuity.

Hints:

In a perpetuity, all cash flows are equal.

Think about what parameter in the first formula goes to infinity.

You can ignore the first term CF $0.$

If proving mathematically, you'll need to use geometric series.