For each of the following series decide if it is Absolutely Convergent, Conditionally Convergent, or Divergent. You must justify all answers. ∞ √In(n) (a) (-1) V n=4 n 3n (b) (2n²±³)³n 3n2-1 n=1 (c) Ĩ n=1 e(n²) 1x5x9...x(4n-3) Q2) AC, CC, D. 124 (-1) √In (n) n consider Elanl Tim n=1 Positive Continuous D Σ √In (n) n=4 n Integral Test decreasing. f(x) = Vin(x) (In(x)) x X f'(x) = (( In (x))". x')- (x + (In(x))"})") x² f'(x) = (In (x)) = (x = (x)/2+) x² f'(x) = (In (x))" - 21m (1) vz X2 21n (x)-1 214(x)/2 'f'(x)=' f'(x) = 2/n(x)-1 2x2 14 (x)2 2n+3 3n 3n²-1 Root test I'm me lank Tim 2n²+33 1700 1137²+ lim 2n²+3 1/2 x² еспа) (×5×9x(4-3) h=1 Ratio Test Tim n->00 an+1 an Tim 1-78 (n+1)² \x5x9x (4(n+1)-3) e(2) 1x5x9(4-3) lim n->x eln t e(n) 1+1)² 1x+x9(4n-3) 1x4x9 (4-3)(4(4+1)-3) Iim (n+1)2 1x519 (4n-3) (4×4) (4+1)² lim 1-700 Tim 1-720 612 (4n+1) x²+2+1 (4+1) (45-3) 11-200 Гом (3n²-1 12+3/20 1-200 .3-46 = 1/n² (를) : 음시 So by Root Test this series is Ac. Tim n->∞ = 2n+1 e (4n+1). Diverges Diverges +∞ > 1 So by Ratio Test This Series