Pre-Calc Homework Solutions 384

Pre-Calc Homework Solutions 384 - 384 Section 9.4 an an (n...

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 384 Section 9.4 an an (n 1)! x 4 n n! x 4 n 1 30. lim n 1 lim n 35. This is a geometric series with first term a common ratio r (x 4 1) 2 1 and (x 4 1)2 . It converges only when lim (n n 1) x 4) 4 1, so the interval of convergence is 3. a 1 r 1 4 x2 x2 1 (x 4 1)2 (x 1 4, so the radius of Sum x The series converges only for x convergence is 0. an an ( 2) n 1 31. lim n 1 lim n (n 2) x 1 2n (n 1) x 1 n n 1 4 (x 1)2 lim 2 x n 1 4 2x 4 2x 3 2x 1 1 3 The series converges for x x 1 an an 1 and diverges for 2 1 1 , so the radius of convergence is . 2 2 36. This is a geometric series with first term a common ratio r (x 9 1)2 (x 9 1)2 1 and . It converges only when 1, so the interval of convergence is 2. a 1 r 1 32. lim n 1 lim n 4x (n 5 1)3/2 2n 3 n 4x 3/2 5 2n 1 4 Sum x lim (4x n 5)2 (4x 5)2 5) 2 The series converges for (4x to 4x x 5 4 an an 1 1, which is equivalent 1 9 (x 9 1)2 5 1 and diverges for 4 1 1 . The radius of convergence is . 4 4 1, or x 5 4 9 (x 1)2 9 2x x2 9 2x 8 x2 8 33. lim n lim n x n n 1 n x n 37. This is a geometric series with first term a common ratio r x 2 x 2 1 and 1 lim x n 1. It converges only when x 0 The series converges for x x an an 1 x 16. a 1 1, so the interval of convergence is 1 and diverges for Sum r 1 1 x 2 2 1 4 x 1, so the radius of convergence is 1. x 2n 2 2n 1 3 34. lim n 1 lim n 2n x 2 2n 1 38. This is a geometric series with first term a common ratio r 1 and 1, 1 (x 2)2 n 2 1 (x 2)2 2 1 The series converges for (x 2 ln x. It converges only when ln x 1 e lim so the interval of convergence is Sum 2)2 1, which is a 1 r 1 1 ln x x e. 39. This is a geometric series with first term a common ratio x2 3 1 1 and x2 3 1 equivalent to x x 2 2 2, and diverges for 2. . It converges only when 2 3 (x 2 1, 2. The radius of convergence is so the interval of convergence is Sum a 1 r 1 1 x2 3 1 x 2. 3 3 1) 4 x2 ...
View Full Document

This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

Ask a homework question - tutors are online