Let {ak} and be real sequences. Decide which of the following statements are true and which are false. Prove the true ones and give counterexamples to the false ones.
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

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(Ak-ak+2) = a1 +a2-2a.