exam_3_s07

# exam_3_s07 - is convergent, nd its limit. 2. Let { p n } be...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
1. Deﬁne the sequence { a n } by setting a 1 = 1 and a n +1 = 1 1 + a n for n 1. Assuming that { a n }
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: is convergent, nd its limit. 2. Let { p n } be the sequence of prime numbers, i.e. { p n } = { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , . . . } . Show that X n =1 (-1) n +1 p n converges. 3. Find a power series representation for the function g ( x ) = x x-5 in powers of x and state for which values of x this representation is valid. 4. Find the interval of convergence of the power series X n =1 x n 3 n n 1 / 2 . Dont forget to check for convergence at the endpoints of the interval! 5. Determine if the series converges or diverges. If it converges, determine if this convergence is absolute or conditional. a. X n =1 (-1) n n + 1 n 3-3 n 2 + 9 n + 13 b. X n =1 n 2 + 1 2 n 2 + 1 n c. X n =2 1 n (ln n ) 2 d. X n =1 (-1) n +1 4 n + 1 e. X n =1 (-1) n n n + 5 f. X n =1 1 5 + (-3) n Calculus II, Exam 3 Work Page...
View Full Document

## This note was uploaded on 02/29/2012 for the course MATH 1312 taught by Professor Ryandaileda during the Fall '11 term at Trinity University.

### Page1 / 3

exam_3_s07 - is convergent, nd its limit. 2. Let { p n } be...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online