(12) Let p 2 1 be a real number. Let an is a sequence so that |sn+1—sn| 3

$ for all n E N.

(a) In the case that p gt; 1 show that SR is convergent.

(b) In the case that p = 1 show that 3n does not have to be conver-

gent. (That is, give an example of 8,1 which is not convergent.

For both parts, you may use any result about series convergence in

the class or in the book. Math