(1) Because you are now privileged math students armed with the power of Calculus II, we are going to settle a conundrum frequently encountered by mathematical lay-people: Is 0.999... = 1?
(a) First, we will need to represent 0.999.. as an infinite series. Do so now.
(b) What are the first three terms of the sequence that you've come up with?
(c) What are the first three terms of the sequence of partial sums related to your sequence?
(d) Think about whether or not the series should converge or diverge (and why), and test your hypothesis by testing the convergence of the series. Be sure to write down your thoughts, and then show your work done in testing the series.
(e) Conclusion: Is 0.999... = 1?