Let {ak} and be real sequences. Decide which of the following statements are true and which are
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a) If ak is strictly decreasing and ak †’ 0 as k †’ ˆž, then ˆ‘ˆžk=1 converges.
b) If ak ‰ bk for all k ˆˆ N and if ˆ‘ˆžk=1 (ak + bk) converges, then either ˆ‘ˆžk=1 ak converges or ˆ‘ˆžk=1 bk converges.
c) Suppose that ˆ‘ˆžk=1 (ak + bk) converges. Then ˆ‘ˆžk=1 ak converges if and only if ˆ‘ˆžk=1 converges.
d) If ak †’ a as k †’ ˆž, then
Transcribed Image Text:
(Ak-ak+2) = a1 +a2-2a.
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a False a k 1k is strictly decreasing to 0 but k1 1k diverges b False The ser...View the full answer
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