Question

Use the Integral Test to determine whether the series is convergent or divergent. oo -5n ne n = 1 Evaluate the following integral. -5x dx 59 xe Since the integral ---Select--- finite, the series is ---Select--- -

Please show ALL work and steps and an explanation as to why the series is convergent or divergent

Answer 1

o The The given series is owi ne-sn n=1 Apply integral test 00 ne-50 dn I the given series is js convergent if the integral I cis finite CO 5n ne-s s Holly integration by party J fgl= fg - ff'g I da co -5n 52 = R -5 5

$[o-1-2-5)- [? e-sh 5 - to [0-4-5) S e-5 5 0-5 e-5 + 5 25 N 5ti 25 x 1 کم aš e5 I ne-snan 60-s 0.0016 the integral uses) is finits the sinu series is Canvergene