408D056 - 784 “II CHAPTER 12 INFINITE SEQUENEES AIID...

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Unformatted text preview: 784 “II CHAPTER 12 INFINITE SEQUENEES AIID SERIES The comparison series for the Limit Comparison Test is 2 b,., where EXAMPLE 3 2 M“ n-I Since the integral I: ate": (1:: is easily evaluated, we use the Integral Test. The Ratio Tes also works. _ co "3 EXAMPLE 4 - " E1 ( l) n4 "I' 1 I Since the series is alternating, we use the Alternating Series Test. _ a: 2‘ EXAMPLE 5 2 — E-l k! Since the series involves k!, we use the Ratio Test. _ EXAMPLE 6 E: 2 + 3" Since the series is closely related to the geometric series 2 1/3", we use the Comparison Test. a! H“ 12.7 Exercises . l-38 llll Test the series for convergence or divergence. ' ln n ' k + 5 I9. -1 " 20. ‘inz—l zin-l ES )Jr'x E. 5* ' ,...l n2 + n ° "-1712 + n 2' i (-2)“ _ 22. i ‘/n2 -l a: I a, "—1 ‘"_I nu n-|"J+2n1+5 3- u _ "-‘ .. a: a: 211:2 + n 4 2:} l) n‘ + n 23 E tan(l/n) 2‘ 2 cos(n/2) °' +| an . n-l . n-l "2 + 4" 52H)" 62( 3" ) .. . 2 n-l 2’" ' n-I 1+8" 25. 2 "‘, 26. 2 " ":1 u: I a 21". IF) 9' n-l 5 7' 2 8. 2 ' x k Ink an 81/- ..-2 n In I: - (k + 2)! . 28. —— , k.‘ 27 E. (k+ n3 "-1 n2 9. E kze" IO. 2 nze‘"3 ‘ tan"): ' , J}: k-l MI] 29- a?! II I! 30- 1;] (—1) j+ 5 a: (—l)"“ an II a: k ’ n - . — " 5 (2n) n g "In" 12 fig} 1) "”25 31. ‘2' 3,”, 32. “T" ” 3"n1 “‘ a - I l . . - sm(l/n) l3 2:: n! , 14 2.5m" 33. 2:] J; 34. Elm “" n! ‘” n2 + l = ,, .8 '° 1 15.n202'5'8'--"(3n+2)‘6'211134-1 35'§.(n+1) 36'§2(lnn)" I E _ n-l x ' l7. 2 (-1)~2'/" l8. 2 I 1) 37. 2(c/i— 1)" 38. 2M”) ...
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