# Marks consider the series s n 1a n where a n 1n 1 ne

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2. [5marks]Consider the seriess=anwherean= (-1)n+1ne-n.(a) Use the Alternating Series Test to determine if the seriessconverges.
(b) Determine the minimum number of terms required insk,thekthpartial sum ofs,so thatskis guaranteedto approximateswithin 0.02.[Hint:bnis decreasing and, therefore, trial and error may be useful.]
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3. [7marks]In the early 1900s, mathematician Srinivasa Ramanujan discovered the series:s=89801Xn=0(4n)!(1103 + 26390n)3964n(n!)4!-1(a) Use the Ratio Test to show that the seriesXn=0an=Xn=0(4n)!(1103 + 26390n)3964n(n!)4converges absolutely.→∞an+1an= limn→∞(4(n+ 1))!(1103 + 26390(