Question 3 (Unit D2) 22 marks (a) Use the definition of a null sequence to prove that the following sequence (an ) is null: (-1)" an 5n4 - 3 n = 1,2. . .. . (b) Determine whether each of the following sequences (a,, ) converges, and find the limit of each convergent sequence. Name any results or rules that you use. You may use the basic null sequences listed in Theorem D7 from Unit D2. 3+ 2n - Ant ) an = 2n4 - n2 - 7 1 = 1.2. . . . 30 + 2(5" ) + 6" ii) an = n = 1.2. ... 3(4") - 507 n + 3(4" ) (iii) an = 3n+ (-1)"47 n = 1.2. . . . marks