1.series convergescorrect2.series divergesExplanation:The functionf(x) =6 ln(2x)x2is continous and positive on [1,∞); in addi-tion, sincef′(x) = 6parenleftbigg1−2 ln 2xx3parenrightbigg<0on [1,∞),fis also decreasing on this interval.This suggests applying the Integral Test, forthen the series∞summationdisplayk=16 ln(2k)k21110.0pointsDetermine the convergence or divergence ofthe series(A)1 +14+19+116+125+... ,and(B)∞summationdisplayn=1ne−n2.1.both series divergent2.both series convergentcorrect3.Aconvergent,Bdivergent4.Adivergent,BconvergentExplanation:

e.Determine whether the series∞summationdisplayk=1k(k+ 2)4kconverges or diverges.