M21Ex3F98

# M21Ex3F98 - 4(6 points Does ∑ ∞ n =1 arctan n converge...

This preview shows page 1. Sign up to view the full content.

Math 21 Exam 3 1. (14 points) For each of the following sequences , determine whether the sequence converges or diverges. It it converges, ﬁnd the limit; otherwise, write DNE and explain why. a) { S n } where S n = n X k =1 2 k +1 - 1 3 k b) ±² n n +1 ³ sin n ´ 2. (12 points) Use the Comparison or Limit Comparison Test to determine whether X n =1 2 n (1 + n 2 ) n 5 +1 converges or diverges. 3. (24 points) For parts a), b), and c) which follow, let b n = ln n n . a) Show that the Integral Test can be applied to n =3 b n . Use this test to determine whether n =3 b n converges or diverges. b) Show that the Alternating Series Test can be applied to n =3 ( - 1) n b n . Use this test to show that n =3 ( - 1) n b n converges. c) Is n =3 ( - 1) n b n conditionally or absolutely convergent? Explain.
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 4. (6 points) Does ∑ ∞ n =1 arctan n converge or diverge? Explain. 5. (18 points) Parts a) and b) that follow refer to the power series ∞ X n =1 (-1) n (2 x + 3) n n 1 / 3 a) Find the interval of convergence for the given power series. b) For what values of x is the given series absolutely convergent? 6. (16 points) In parts a) and b) which follow, for | x | < 1 let f ( x ) = 1 1-x = ∑ ∞ n =0 x n . a) Find the power series, ∑ ∞ n =1 c n x n , equal to xf ( x ). b) Find the power series, ∑ ∞ n =0 b n x n equal to Z x 1 1 + t 4 dt. 7. (10 points) Find the Taylor series at a = 2, for f ( x ) = 1 x . 1...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online