# MATH262_MAY2016.Assignment1 - Omid Makhmali due at 11:59pm...

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Omid MakhmaliAssignment Assignment1MATH262, May 2016due 05/10/2016 at 11:59pm EDT..1.(1 point)Library/ASU-topics/setCalculus/stef/stef11_1p1.pgFind a general term (as a function of the variable n) for thesequence{a1,a2,a3,a4,...}={34,916,2764,81256,...}.an=Correct Answers:(3/4)**n2.(1 point)Library/./maCalcDB/setSequences2Limits/ur_sq_2_23.pgFind the limit of the sequence whose terms are given byan=1e4n+n21/n.Correct Answers:0.01831563888873423.(1 point)Library/Michigan/Chap9Sec1/Q19.pgMatch the formulas with the descriptions of the behavior of thesequence asn.1.sn= (n+1)/n2.sn=3-1/n3.sn=1/(n+1)4.sn=1-n2 5.sn=3+(-1)n/(n) A. converges to three from above and belowB. diverges to-C. converges to three from belowD. converges to zero through positive numbersE. converges to one from aboveSolution:( Instructor solution preview: show the studentsolution after due date. )SOLUTIONThe correct behaviors are 1 matches E, 2 matches C, 3matches D, 4 matches B, and 5 matches A.Correct Answers:ECDBA 4.(1 point)set2/setSeries4Geometric/ur_sr_4_1.pgThe following series are geometric series.Determine whether each series converges or not.For the series which converge, enter the sum of the series. Forthe series which diverges enter ”DIV” (without quotes). n=18n7n=,n=213n=,n=03n52n+1=,n=57n8n=,n=17n7n+4=,n=17n+3n8n=.Correct Answers:DIV0.1666666666666670.2272727272727274.103271484375DIV7.65.(1 point)set2/setSeries2Telescope/ns8_2_21.pgIf the following series converges, compute its sum. Otherwise,enter INF if it diverges to infinity, MINF if it diverges to minusinfinity, and DIV otherwise.n=12n(n+2)(Hint: try breaking the summands up partial fractions-style.)Correct Answers:1.56.(1 point)set2/setSeries2Telescope/ns8_2_24.pgFor the following series, if it converges, enter the limit of con-vergence. If not, enter ”DIV” (unquoted).n=1ln(2(n+1))-ln(2n)Correct Answers:DIV 1
7.(1 point)set2/setSeries5IntegralTest/eva8_3_1.pgCompute the value of the following improper integral if it con-verges. If it diverges, enter INF if it diverges to infinity, MINFif it diverges to minus infinity, or DIV otherwise (hint: integrateby parts).Z15ln(x)x2dxDetermine whethern=1(5ln(n)n2)is a convergent series. Enter C if the series is convergent, or Dif it is divergent.Correct Answers:5C8.(1 point)set2/setSeries5IntegralTest/eva8_3_2.pgFind the value ofZ2dx4x(ln(9x))2Determine whethern=2(14n(ln(9n))2)Enter A if series is convergent, B if series is divergent.Correct Answers:0.0864940640652984A9.(1 point)set2/setSeries3Convergent/ns8_3_7.pgMatch each of the following with the correct statement.