Problem 1. Let O+8 be a positive sequence, and assume that the following limit exists:

8A_ ln8 a) If = ", show that !+8 converges.

8" _

b) If = ", show that !+8 diverges. 8"

c) Give an example of a sequence where = ", and the sum diverges. d) Give an example of a sequence where = ", and the sum converges.

Problem 1. Let {an} be a positive sequence, and assume that the following limit exists: _ In an 11m = s. Try>00 1n n a) If s 1, show that 2 an diverges. n=1 c) Give an example of a sequence where s 2 1, and the sum diverges. (1) Give an example of a sequence where s 2 1, and the sum converges