Directions: As always, show work, show reasons, and justify everything. 1. Decide whether or not the given infinite series converges or diverges. You must justify your answer using the standard tests discussed in class. If it converges. then decide whether it converges conditionally or converges absolutely. Do not try to calculate the actual value of the infinite series. Show all justification. (a) n2 n= 2 n' + 3n + 1 ( b ) 4" By the antl nai (2n)! limit comparison tesfunparker ratio Test an 3 ( AT1 ) - 4 n tant ( anti ) ! ur na na stchet converse . = 1 antlie n Because the absolution equator =!1/ we cannot say not true LI converses absoluteX ( c) >, 1 so it is conditionally n(In n) (d) n=1 723/2 5 ( - 1 )" use AT fort! 2 n=1 318 -7 Integra test (at1 13id . V = incn) (-I)' ntl L ( 1 ) 3/2 (niti ) 812 h ( nt1 ) 312 2 ) Because the denominaor n 312 In bro is larger,we car inlin(n ) safely assvive that This ewration is true . - lim absolutcy -7 Inlin cool - Q) 1700 312 = 0 Conversig oo diversent -7 (-12 1 20 V conversent