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“ nI 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 —
El 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 . l38 llll Test the series for convergence or divergence. ' ln n ' k + 5
I9. 1 " 20.
‘inz—l zinl 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 . nl . nl "2 + 4"
52H)" 62( 3" ) .. . 2
nl 2’" ' nI 1+8" 25. 2 "‘, 26. 2 " ":1
u: I a 21". IF) 9' nl 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}:
kl 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)‘6'2111341 35'§.(n+1) 36'§2(lnn)"
I E _ nl x '
l7. 2 (1)~2'/" l8. 2 I 1) 37. 2(c/i— 1)" 38. 2M”) ...
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 Fall '07
 Sadler

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