part a
jimmy has a new job and plans to start saving some money. he decides to use his knowledge of geometric series to set up a savings plan that will start off with him setting aside a small amount each week, and end with him saving a large amount. in each of the first 5 weeks of his job, he wants to raise $2 to the number of weeks he has been working, multiply it by 3, and add that amount to the savings account. use summation notation to write this as a sum and find the total amount jimmy will save in 5 weeks.
part b
one of jimmy’s friends told him that he would save more if, instead of multiplying the amount by 3 each week, he added enough at the end of 5 weeks to multiply the existing amount by 3. use summation notation to write this as a sum and find the total amount he would save using this
part c
would jimmy save more money by following the second plan? how do the amounts compare?
part d
generalize the property of summations shown by the results of parts a and b.
part e
now jimmy wants to save money to buy concert tickets, so he draws up a new savings plan. each week, he will raise $3 to the number of weeks he has been working and add that amount to his savings during the first 3 weeks of his new job. use summation notation to write the sum and find the total amount he will save.
part f
jimmy’s friend tom also wants to save money to buy concert tickets. he draws up the following savings plan. each week tom will raise $4 to the number of weeks he has been working and add that amount to his savings during the first 3 weeks of his new job. use summation notation to write the sum and find the total amount tom will save in three weeks.
part g
find the total amount of money jimmy and tom will save together.
part h
now, add the total amount of money that jimmy and tom will save together each week for 3 weeks. then find the sum of the amounts obtained for each of the 3 weeks.
part i
how do the total amounts calculated using the two methods compare?
part j
generalize the property of summations shown by the results of parts g and h.