Stepwise problems - Thu. 11:59pm
Positive series
01
02
Link to originalDirect 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)
02
03
Link to originalLimit 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.
Alternating series
03
01
Link to originalAbsolute 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)
Ratio test and Root test
04
01
Link to originalRatio 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)
Regular problems - Sun. 11:59pm
Positive series
05
05
Link to originalIntegral 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:
06
06
Link to originalLimit 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.
Alternating series
07
02
Link to originalAbsolute and conditional convergence
Determine whether the series are absolutely convergent, conditionally convergent, or divergent by applying series tests including the Alternating Series Test.
Show your work. You must check that the test is applicable.
(a)
(b)
08
03
Link to originalAlternating series: error estimation
Find the approximate value of
such that the error satisfies . How many terms do you really need?
Ratio test and Root test
09
02
Link to originalRatio 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)