# Where every other negative term is moved up to be

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(b) Use Maple to determine the sum of each series (see # 1(b) for code).
(c) Considering parts (a) and (b), is the seriessabsolutely convergent, conditionally convergent, or divergent?Explain.
3. [3marks]Consider the seriess=Xn=1-3n2 +n4n.Using the Root Test, determine whether the series isabsolutely convergent or divergent.limn→∞nvuut-3n2 +n4n= limn→∞3n2 +n4= limn→∞34n4(2 +n)4= 81 limn→∞n4(2 +n)4÷n4÷n4= 81 limn→∞1(2+nn)4= 81 limn→∞1(2n+ 1)4= 81>1the series diverges by the Root Test.4. [10marks] Consider the seriesn=2(-1)n(2x+ 3)nnlnn. For each of the following values ofx, determine whetherthe resulting series converges absolutely, converges conditionally, or diverges.(a)x=-3n=2(-1)n(2x+ 3)nnlnn=n=2(-1)n(-3)nnlnn=n=23nnlnnwhich diverges by the Test for Divergence:limn→∞an= limn→∞3nnlnnI.F.=Hlimn→∞3nln 3lnn+ 1I.F.=Hlimn→∞3n(ln 3)21/n= limn→∞n3n(ln 3)2=(b)x=-1[You may use Maple to find any derivatives or integrals:diff(???,x); simplify(%);int(???,x=?..?);]n=2(-1)n(2x+ 3)nnlnn=n=2(-1)n(1)nnlnn=n=2(-1)nnlnn
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