MATH103WEBWORK11.pdf - Math 103 web work 11 I q I Ir ¥ ta...

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Math 103 web work 11 I ¥ q , ¥5 a - - E , r - - Ez , re ' diverges . I , qq.sc#n.a= # Is , r - - I , s - - HI \ - 7/8 BEEN a - - ¥ - - ta i r - - I . S - - Ir - - II , " ; e) £ , 3 = § , 's . - ( 35 , r z I diverges a ?i÷÷ . E.tt#5ia--Eir-z.is= . . ' ' i , " E . . E. it E. i ;I÷t¥ . E. z÷± E. Fort E. ' n - - %tF÷ . Oz divergence test : an = 52 and things an = linney g5÷z = Sf to , so series diverges . Sent 7 QI n , nn-tz.nl?aan--nhhhsnn-+z-- I to , so by divergence test , series diverges . An = ht . Bn = they , Cn = In . we know By p test An , Bn converges and Cn diverges . ing , 7nn ' for large n this will behave like y2n÷ , = In , comparing to Cn = In , In < in 4nF + Gns - y ' since they are of some form , we can use Limit comparison Test , an = In , bn - - th and nhjmp FIN = Lz so so both an and bn have same Nature . Now since bn In diverge , so In must also diverge 2) , 2n4tn2-2# , for large n , This behaves like 2gnn = ¥ , comparison to Aunt , we can apply 8h " - 7n9 +9 limit comparison test , things %t , = I > o , so both have same behaviour , because ntz converge Direct comparison will work too !
Then In , will also converge . 3 . , Y%}tfny+ , for large n , behaves like , Gysin , , = , by . So compare it to Bn =L . In a direct comparison 16¥ C ÷ and thy converges , so , ggtzny will also converge 1) , Gio .

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