Question

1. Let {an}, be a sequence. Write down the formal definition of the following con- cepts. You have already seen some of these in lecture (a) The sequence is convergent b) The sequence is divergent. (c) The sequence is divergent to oo (d) The sequence is divergent to -oo (e) The sequence is increasing f) The sequence is decreasing (g) The sequence is non-decreasing (h) The sequence isn't decreasing (i) The sequence is bounded above (j) The sequence is not bounded above (k) The sequence is bounded Hints: Are all your variables introduced or properly quantified in Question la? Questions le, 1g and lh all have different answers.

Answer 1

"{a_n}^infinity_n = 1 b subset a sequence (a) exist x (exist for all elementof 0, exist n, elementof N exist

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