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Math 106 BC Quiz 06 page 1 11/12/2010 Name_Svqgastedk soluhon Circle your Section: —_B (1lam) C (noon) 3k-1 la. What are the first four terms of the sequence? 1. Consider the sequence {a,}22, given by a, = 2 & 26 § 354 2Py 8| 1b. What is the limit L of this sequence? (*) lc. Find N such that |ay —L| is not less than ¢ = 0.001 but ifn > N, then Jan — L| 26.'8.. 3% WV: 25) 2a. Using the notation developed in aaa, find a and r for the following geometric series: fp. 80 + 32 + 64/5 + 128/25 + 256/125 + --- fh gi & geome sits, ber r caliber Mr =$2, rae St, oh, ort Se wa 8 60 fos” = 2b. What's the next term in the series? 256 2 S!2 Qa, =2Q jas (5 625— Kel Sae x 2c. Does the series in (2a) converge? If so, to what? tne lel, am aneeye, = Se Or Tay 2d. If the “80” was not actually the first term of the earls, what would the term in front of it be? Coll Pot. rv erm T, sme Ta = 90, we ave T= £. 30° s1o=foo | 3a. Explicitly, what is the harmonic series? (give the first 5 terms). [++ Ar hy + ote 3b. It’s a fact that if a series va converges, then the “individual terms” a1, 2, a3, @4 ... have to “go to zero”. What does the harmonic series have to 0 with the converse of this “y The Gantt of te het : "of the mypenec Oy Bs, ha toit fC) tan Cortegondiy Serwes Q, +4, +4q¢~ conus Bud thi Stale rod 1 ‘lee al. urine sents » He ca aitraconle: En ay te cegtrce Vth 3, -_ the serks (+e ter... DWE 
