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408D054 - fi— 660 I CHAPTER ll INFINITE SERIES Example 7...

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Unformatted text preview: fi— 660 I CHAPTER ll INFINITE. SERIES Example 7 For the series a“l 1 2k+l 2k+l 2+1/k Therefore, we have to look further. Comparison with the harmonic series shows that the series diverges: _;. .. = _— —-> —- and 2 idiverges. Cl ‘ Summary on Convergence Te In general, the root test is used only if powers are involved. The ratio test is partic- ularly effective with factorials and with combinations of powers and factorials. If the terms are rational fimctions of k, the ratio test is inconclusive and the root test is difficult to apply. Rational terms are most easily handled by comparison or limit comparison with a p-series, E 1 /kP. If the terms have the configuration of a derivative, you may be able to apply the integral test. Finally, keep in mind that, if at + 0, then : there is no reason to apply any special convergence test; the series diverges by The- orem 11.1.7. 1:“:‘ LI”; EXERCISES ”.3 :71" “1;... _______________————-—-—-———————'—— 1;...“ In Exercises [—40, determine whether the series converges or ' k (“)2 diverges. (/21. 2 ( k + 100) . 22. (—27)? 1- 2 “1%. 2- E 7:127.- 23. 2 k'“*“"). 24. 2 1 +2100”. 3- 2 fi- 4- 2 (2k: ])k- 25. 13;. 26. 2%. 5 2 73:):- _6..- Z (Inkky. 27. 2 la?" 2 . 4“" 7° 21: :62k 8' 2(ln1k)" 28- 2 1.3....512,‘ _ l)’ 9‘ 2 k (9* 10- 2 (mlk .o- 29. 2 13%. '30. 2 $721231;- ‘1 2 l +lfl 112:6:fi-31. %2k—I)‘!)—!. 32. 2%;- 13. 2 % 14. 2 I; 33. Z 552—. 34- Z R ° 15; 2 szE 1‘ 16. 2 1k? 35, 2 %_ 36. 17-21%?” "3-2;: “+037 37.%+-32—2+%+%+~ l - l - 2 ' 3 l 2 ' 3 ' 4 38. ...
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