Originally Posted by

**tttcomrader**

#3. Let a1 = 4. Define an+1 = an/2 + 2/an , for n = 1,2,3,...

a) Evaluate a2, a3, a4.

b) Prove that if an > 2, then an+1 > 2. use induction to prove that an > 2 for all n within the set of Natural Numbers.

c) Prove that an+1 <= an for all n within the set of Natural Numbers.

d) Is {an} bounded? If so, find A,B of R such that A <= an <= B for all n within N.

e) Does lim (n->inf) an exist? Why?

My solution: I'm currently still reading the text in attempt to find the answer.

Finally, I understand that these problems are hard and would reqire some work to finish, but if you can as much as give me some hints I would really appreicate it!!!

Thank you!