1) Give an example of a sequence {a_n} that converges but where the sum of the seriesdiverges.Use this to explain the test for divergence and the difference between a sequence converging and a series converging.

2) (This is a good one to choose if you are interested in computer science!) Research the growth of functions. Some functions grow faster than others. How can this hierarchy help you decide if a sequence converges or diverges? In particular, thinkabout functions which are theratios of two functions, such as. How does looking at the growth of the numerator and denominator help you understand the convergence and divergence of the sequence?