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MAT 146 - Tests for Convergence (Final Exam)
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MAT 146 - Tests for Convergence (Final Exam)
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MAT 146 - Tests for Convergence (Final Exam)ar^(n-1), cgt if |r|<1 - ANS-What is a geometric series? When is it convergent?
a/(1-r) - ANS-What is the sum of a geometric series?
G.S., integral test, definition of cgt/dgt series - ANS-What 3 tests can you use to find the sum of
a series?
1/n, always dgt - ANS-What is a harmonic series? Is it cgt or dgt?
lim (as n approaches infinity) of an
-DNE = dgt
-exists and doesn't equal 0 = dgt
-inconclusive if =0 - ANS-What is the test for divergence (TFD)?
lim (as n approaches infinity) of Sn
-exists = cgt
-DNE = dgt
Sn is sum of series (write out all terms) - ANS-How do you determine convergence with
definition of cgt/dgt series?
Can only use if f(n) is continuous, positive, decreasing on [1,infinity)
then, cgt if integral (from 1 to infinity) is cgt
dgt, if integral (from 1 to infinity) is dgt - ANS-How do you determine convergence with the
integral test?
-geometric series
-harmonic series
-definition of cgt/dgt series
-TFD (test for divergence)
-integral test
-comparison test
-limit comparison test
-ratio test
-root test
-p-series test
-p-alternating series test
-Alternating series test - ANS-Name the 12 tests
build your own series
-if bigger cgt, then smaller cgt
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