1. Section 11.4 Infinite Geometric Series

2. Let’s revisit our fast-food example where the restaurant sold 50,000 sandwiches the first month and their sales decreased by 20% each month –We found out how many they sold for one year –What will happen in the long run if the trend continues? –We know that for n months we have the equation –Let’s see what happens as n gets large

3. We know from our work with exponential functions that if |r| < 1, then r n → 0 as n → ∞ Therefore, whenever |r| < 1, the sum of the infinite geometric series is given by Now if |r| > 1 then we say the infinite geometric series does not converge What if r = ±1? It still will not converge (in other words, it will still not approach a certain number)

4. Present Value of a Series of Payments When a sum of money is to be paid out over time, it has what is called a present value For example, when an individual wins the lottery, they have the option of taking their money in a series of payments totaling their winnings (less taxes). Therefore the state does not have to have all the money present. The amount they need present in order to make the appropriate payments is the present value of the money.

5. Recall that B = P(1 + r ) n The question is what amount do we need, P, in order to have a balance of B after n years? So we use Let’s see how this works Suppose the recent lotto winner has agreed to accept annual payments of $300,000 and the state can get 5% annual interest What would be the present value of 5 payments? What about of 30 payments? What if they continued forever?