Stepwise problems - Thu. 11:59pm
Positive series
01
Integral Test (IT)
Use the Integral Test to determine whether the series converges:
Show your work. You must check that the test is applicable.
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)
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.
Alternating series
04
Absolute and conditional convergence
Apply the Alternating Series Test (AST) to determine whether the series are absolutely convergent, conditionally convergent, or divergent.
Show your work. You must check that the test is applicable.
(a)
(b)
Regular problems - Sat. 11:59pm
Positive series
05
Integral Test (IT)
Determine whether the series is convergent by using the Integral Test.
Show your work. You must check that the test is applicable.
(a)
(b)
(c)
06
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:
07
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.
Alternating series
08
Absolute 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)
09
Alternating series: error estimation
Find the approximate value of
such that the error satisfies . How many terms do you really need?