Need help with arithmetic/geometric series
Some people believe they can make money from a chain letter (they are usually disappointed). A chain letter works roughly like this: A letter arrives with a list of four names attached and instructions to mail a copy to four more friends and to send 1 to the top name on the list. When you mail the four letters, you remove the top name (to whom the money was sent) and add your own name to the bottom of the list.
a) If no one breaks the chain, how much money do you receive?
b) Let d sub n be the number of dollars you receive if there are n names on the list instead of 4, but you still mailed to four friends. Find a formula for d sub n.
Please help me with this confusing problem. Also show your work and explain how you got to the answer. Thank you so much!