08.01 - 8.1 SEQUENCES ._("1)2__ (—1)3__1...

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Unformatted text preview: 8.1 SEQUENCES ._("1)2__ (—1)3__1 _(—1)4_1 _(—1)5__1 3 31—2—1 1’32—4—1— 3'33—6—1—5'34—8—1— '7 _ W 1W3 W3 1W7 W7 1m15 W15 1_31 _63 7 al—1,32—1+§—§,33—§+§z—3,a4—3+§5—f,35—f+§;—fi,a6—fl, 127 255 __ 511 _ 1023 a7_fi’a ‘fi’a9—2T’310— 12 11. a1_Lag-1,33—1+1—2,a4_2+1—3,a5—3+2—5,afi—8,a7_13,ag_21,ag—34,a10:55 15. all z (—1)“+1n2, n = l, 2, 19. anz4n—3,n=1,2,... 23. n [gum 2 + (0.1)“ 2 2 2} converges (Theorem 5, #4) ' l—an - (i)—2W . _2W_ 25' 11131100 l+2n ‘nleoo (ff; 2 -H_,moo T — 1 2> converges 1 ' l—Sn‘ __ - (1:7)“.5 __ _ 11!me 1114-8115 _n!Lm°o 1+”) — 5 => converges 29. lim w: lim w: lim (n—1)=oo :diverges “.500 n 1 11—100 11 l n——>oo ("Fun-H Zn— 1 - l2 __ / - 2 _ - 2 __ 37. "1351100 “:1- "13411100 n:1_\nlem (m)_\/§:>converges 41. lim Sin—" 2 0 because — i 5 ’1“ S 3-1 => converges by the Sandwich Theorem for sequences 31. lim (1 + (—1)”) does not exist => diverges 35, “131100 2 0 2“) converges - ln(n+l) __ - n __ ' _.._ ' .... 45. In11in00 7;— —nl_g'nCJO 7%? —ngmm n+1—n_’m00 m —0 => converges 47. nlwimigr}co 8”“ = 1 => converges (Theorem 5, #3) 49. lim (1 + 3-1)“ = e7 :> converges (Theorem 5, #5) - n! __ - 1-2'3"-(n-1)(n) - 1 __ n! - n! __ 59. “131100 a; —nleoo SEIng (a) —0and 11—“- 20 => nleoo a; —0 => converges ...
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08.01 - 8.1 SEQUENCES ._("1)2__ (—1)3__1...

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