W09 - Homework

Stepwise problems - Thu. 11:59pm

Positive series

01

02

Direct Comparison Test (DCT)

Determine whether the series is convergent by using the Direct Comparison Test.

Show your work. You must check that the test is applicable.

(a) (b)

Link to original

Solution

Solutions---0180-02

02

03

Limit Comparison Test (LCT)

Use the Limit Comparison Test to determine whether the series converges:

Show your work. You must check that the test is applicable.

Link to original

Solution

Solutions---0180-03

Alternating series

03

01

Absolute and conditional convergence

Determine whether the series are absolutely convergent, conditionally convergent, or divergent.

Show your work. You must check applicability of tests.

(a) (b)

Link to original

Solution

Solutions---0190-01

Ratio test and Root test

04

01

Ratio and root tests

Apply the ratio test or the root test to determine whether each of the following series is absolutely convergent, conditionally convergent, or divergent.

(a) (b) (c)

Link to original

Solution

Solutions---0200-01

Regular problems - Sun. 11:59pm

Positive series

05

05

Integral Test, Direct Comparison Test, Limit Comparison Test

Determine whether the series converges by checking applicability and then applying the designated convergence test.

(a) Integral Test:

(b) Direct Comparison Test:

(c) Limit Comparison Test:

Link to original

Solution

Solutions---0180-05

06

06

Limit Comparison Test (LCT)

Use the Limit Comparison Test to determine whether the series converges:

Show your work. You must check that the test is applicable.

Link to original

Solution

Solutions---0180-06

Alternating series

07

02

Absolute and conditional convergence

Determine whether the series are absolutely convergent, conditionally convergent, or divergent by applying series tests.

Show your work. You must check that the test is applicable.

(a) (b)

Link to original

Solution

Solutions---0190-07

08

03

Alternating series: error estimation

Find the approximate value of such that the error satisfies .

How many terms do you really need?

Link to original

Solution

Solutions---0190-03

Ratio test and Root test

09

02

Ratio and root tests

Apply the ratio test or the root test to determine whether each of the following series is absolutely convergent, conditionally convergent, or divergent.

(a) (b) (c)

Link to original

Solution

Solutions---0200-02