I have the following problem:
The number of customers in the first year is 4000. Each year the number of cuatomers increases by 1000 (t1=4000,t2=5000...tn=3000*1000n). Farther, each customer is to pay an annual fee F. r is thd interest rate. I got to find the cash value of the aernings of this company in year t.
The cash value of the earnings in year t is (3000+1000t)F/r^t.
The whole cash value until year t is the cash value of every year until year t added, thus
This equals F(4000r^(t-1)+5000r^(t-2)...+3000+1000t)/r^t
If you leave by side F/r^t, i need to find the sum of 4000r^(t-1)+5000r^(t-2)...(3000+1000t)r^0. however i dont get how to do it, as rhis is a mixture of the arithmetric series 3000+1000t and the geometric series r^t.
Anyone knows how to do that?