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Practice_Exam2

Practice_Exam2 - Practice Test For The Benet of Mr Kite...

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Practice Test For The Benefit of Mr. Kite David Imberti April 16, 2010 1 Disclaimer The stuff in here should be correct. But I didn’t copy this from somewhere. It’s coming straight from me bashing on a keyboard for the past three or four hours. So if you spot any errors or have any confusion, let me know so I can correct it. Others are studying from this. But other than this worrying disclaimer, I’m pretty sure the stuff in here is spot-on. So don’t worry about it. 2 Warm-up Problems: Not Lava. More like a hot bath in Tokyo. SPOILER WARNING: The following are worked out as example in the discussions that follow. I included more bonus problems after these discussions. Do the following converge or diverge? (0) Σ n =1 sin ( n ) n 2 (1) Σ e - n n . (2) Σ q n n +1 . (3) Σ n 1 n + n 2 Σ n 1 n 2 . (4) Σ n =3 ln ( n ) n . (5) Σ n =1 ( - 1) n 25 e n (2 n +3)! . (6) Σ n =1 1 ln | n | . (7) Σ n =1 1 7 n 8 +30000 n . (8) Σ n =1 (1 + 1 n + 1 n 2 ) 25 e - n . (9) Σ n =1 (1 + 1 n ) n 2 . (10) Σ n =1 ln ( n ) n . Are the following Absolutely Convergent, Conditionally Convergent, or Divergent? (11) Σ n =0 10 - n . (12) Σ n =3 ( - 1) n ln ( n ) n . (13) Σ n =1 ( - 1) n n +1 nln ( n ) . (14) Find the minimal number of terms one needs to sum to approximate the convergent alternating series Σ n =2 ( - 1) n n ! to an error of less than or equal to 1 120 . Find the Interval of Convergence of the following. (15) Σ n =0 x 2 n (2 n +2)! . (16) Σ n =0 n ! x n . (17) Σ n =0 | x - 3 | n . (18) Simplify the sum Σ n =0 x n + Σ n =1 x n - 1 . 1

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