final_solutions_21c_18.pdf - CALCULUS Math 21C Spring 2018...

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CALCULUS:Math 21CSpring 2018: Final ExamSolutions1.[10 pts] Do the following series converge or diverge? State clearly whichtest you use.(a)Xn=11pn(n+ 1)(n+ 2)(b)Xn=1(-1)ncos1nSolution.
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2.[20 pts] Determine the interval of convergence (including the endpoints)for the following power series. State explicitly for what values ofxthe seriesconverges absolutely, converges conditionally, or diverges. Specify the radiusof convergenceRand the center of the interval of convergencea.Xn=0(-1)nn+ 1(x+ 2)n.

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