Look at the formula for the present value of an annuity. What happens to the present value

Question:

Look at the formula for the present value of an What happens to the present value as the number of periods increases? What distinguishes an from a perpetuity? Why is there no formula for the of a perpetuity?
Annuity
An annuity is a series of equal payment made at equal intervals during a period of time. In other words annuity is a contract between insurer and insurance company in which insurer make a lump-sum payment or a series of payment and, in return,... Future Value
Future value (FV) is the value of a current asset at a future date based on an assumed rate of growth. The future value (FV) is important to investors and financial planners as they use it to estimate how much an investment made today will be worth...