1103 26390 n lim n 4 n 427493 26390 n 396 4 n 4n 14 396 4n n 4 4 n 1103 26390n

1103 26390 n lim n 4 n 427493 26390 n 396 4 n 4n 14

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(b) Defines=9801as a series in Maple:a(n):=???;s(k):= ((sqrt(8)/9801)*sum(a(n),n=0..k-1))(-1);To 9 decimal places, evaluate each of the following partial sums using Maple.i.s1.= 3.141592729s(1); evalf(%);(ii)s5.= 3.141592653Look familiar? 4. [2marks] For each of the following series, explain which convergence test you would apply and why.[Note: You do not need to actually apply the test or determine whether the series is convergent or divergent.More than one answer may be possible.](a)Xn=1enn2Can use the Test for Divergence sincelimn→∞an6= 0.Can use the Ratio Test, since the series involves a constant raised to thenth power.(b)Xn=1n2e-n3Can use the Integral Test sinceR1x2e-x3dxis easily evaluated.Can use the Ratio Test, since this series involves a product, but not a rational oralgebraic function ofn.Grade:2020

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