a) For all n>1,01nlog(n)<2n, and the series 2n=11n diverges, so by the Comparison Test, the series n=21nlog(n) diverges.b) For all n>1,n5-n3<1n2, and the series n=11n2 converges, so by the Comparison Test, the series ==1n5-n3 cormerges.c) For all n>1,0arctan(n)n3<2n3, and the series 2n=11n3 converges, so by the Comparison Test, the series i=1arctan(n)n3 converges.d) For all n>2,n12n>1n0, and the series n=11n diverges, so by the Comparison Test, the series n=1n12n diverges.e) For all n>2,0nn3-4<2n2, and the series 2n=11n2 comverges, so by the Comparison Test, the series n=1nn3-4 converges.For all n3,01n2-5<1n2, and the series n=11n2 converges, so by the Comparison Test, the series n=11n2-5 converges.