Determine whether each statement below is true or 1 (circle one). Provide a brie

Question

Determine whether each statement below is true or 1 (circle one). Provide a brief justification or counterexample for each statement. 2 points for each correct true/false, 2 points for the justification/counterexample. (a) If the terms a_n,n = 1, 2, 3,... of an infinite series satisfy lim_N rightarrow infinity a_n = 0, then sigma_n=1^infinity a_n converges. The series sigma_n=1^infinity converges absolutely for all real numbers x Assume a_n and b_n, n = 1, 2, 3,. are the terms of two infinite series and 0 lessthanorequalto a_n lessthanorequalto b_n for all n Greaterthanorequalto 1. If sigma_n=1^infinity a_n diverges, then sigma_n=1^infinity b_n must also diverge.

Explanation / Answer

a)

true

b)

false

c)

true

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