Do [5] 5. (a) Show that converges to a real number. n=1 (2n2)! 10n [3] (b) What is the value of lim 1-+00 (2n)! (Hint. Use part (a) of the question). 6. Determine whether the following series converge to a real number or not. [5] (a) > sin (tan(n2)) n2 n=1 [5] (b) > sin(- n=1 7. Briefly justify your answers to the following statements. [2] (a) Give an example of a sequence {an} such that lim an = 0 but > an is divergent. n=1 (2] (b) Give an example of a series > an which is absolutely convergent but not condi- n=1 tionally convergent. [2) (c) Give an example of a series ) an which is conditionally convergent but not abso- n=1 lutely convergent