Question 1 - Infinite Sequences.
(a). Determine an infinite sequence that satisfies the following .. .
(i) An infinite sequence that is bounded below, decreasing, andconvergent
(ii) An infinite sequence that is bounded above anddivergent
(iii) An infinite sequence that is monotonic and converges to 1as n ? ?
(iv) An infinite sequence that is neither increasing nordecreasing and converges to 0 as n ? ?
(b). Given the recurrence relation an = an?1 + n for n ? 2 wherea1 = 1, find a explicit formula for an and determine whether thesequence converges or diverges
(c). Find a explicit formula for an given that {an}? n=1generates the infinite sequence 1, ? 1 9 , 1 25 , ? 1 49 , . . .Does the above infinite sequence converge or divergence?
