The nth term of a series is represented by an=4n5n+1⋅n . Otto correctly applies the ratio test to determine whether the series converges or diverges. Which statement reflects Otto's conclusion? A From the ratio test, r = 0.8. The series diverges. B From the ratio test, r = 0.8. The series converges. C From the ratio test, r = 0.32. The series diverges. D From the ratio test, r = 0.32. The series converges.

Can someone me with this problem . show your work .

Solve: 25 points find the fifth term of an increasing geometric progression if the first term is equal to 7−3 √5 and each term (starting with the second) is equal to the difference of the term following it and the term preceding it.

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?