below 21. All face cards (jacks, queens, and kings) are worth 10 points, and an ace in blackjack is wortheither 1 or 11 points. The students used the professor’s strategy along with a card-counting technique toplace higher bets when there were more high-value cards left in the deck.It is reported that in 1992 the team won $4 million from Las Vegas casinos. The casinos caught on, andthe students were all banned within 2 years. The 2008 movie 21was based on this event.23456Dealer’s Up CardA BASIC STRATEGY FOR BLACKJACKWhen surrender is allowed, surrender 9, 7 or 10, 6 vs 9, 10, A; 9, 6 or 10, 5 vs 10When doubling down after splitting is allowed, split: 2’s, 3’s, 7’s vs 2-7; 4’s vs 5 or 6; 6’s vs 2-678910ASSSSSSSSSSSSSSSHHHHHSSSSSHHHHHSSSSSHHHHHSSSSSHHHHHHHSSSHHHHHDDDDDDDDDHDDDDDDDDHHHDDDDHHHHHHHHHHHHHHHSSSSSSSSSSSDDDDSSHHHHDDDDHHHHHHHDDDHHHHHHHDDDHHHHHHHHDDHHHHHHHHDDHHHHHSP SP SP SP SP SP SP SP SP SPSSSSSSSSSSSP SP SP SP SPSSP SPSSSP SP SP SP SP SPHHHHHSP SP SP SPHHHHHDDDDDDDDHHHHHHHHHHHHHHSP SP SP SPHHHHH17+1615141312111095 - 8A, 8 - 10A, 7A, 6A, 5A, 4A, 3A, 2A, A; 8, 810, 109, 97, 7IIIIIIYour HandIV6, 65, 54, 43, 32, 2HSP SP SP SPHHHHITSTANDDOUBLE DOWNSPLITHSequences, Series, and Probability12
■Find the general nth term of a sequence or series.■Evaluate a finite arithmetic series.■Determine if an infinite geometric series converges or diverges.■Prove a mathematical statement using induction.■Use the binomial theorem to expand a binomial raised to a positive integer power.■Understand the difference between permutations and combinations.■Calculate the probability of an event.L E A R N I N G O B J E C T I V E SIN THIS CHAPTERwe will discuss counting and probability in addition to three other topics: sequences andseries, mathematical induction, and the binomial theorem.• Sequences• FactorialNotation• RecursionFormulas•Sums andSeries• ArithmeticSequences•The General(nth) Termof anArithmeticSequence•The Sum of anArithmeticSequence• GeometricSequences•The General(nth) Termof aGeometricSequence• GeometricSeries• MathematicalInduction• BinomialCoefficients• BinomialExpansion• Pascal’sTriangle•Finding aParticularTerm of aBinomialExpansion• TheFundamentalCountingPrinciple• Permutations• Combinations• PermutationswithRepetition• SampleSpace• Probabilityof an Event• Probabilityof an EventNotOccurring• MutuallyExclusiveEvents• IndependentEventsSEQUENCES, SERIES, AND PROBABILITY12.1Sequencesand Series12.2ArithmeticSequencesand Series12.3GeometricSequencesand Series12.4MathematicalInduction12.5TheBinomialTheorem12.6Counting,Permutations,andCombinations12.7Probability1217
SequencesThe word sequence
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- Summer '17
- juan alberto
- Arithmetic progression, Geometric progression, Conic section, general term, graphing utility