# 55 - Chapter at Review 55 General Berrievv Guide Chapter 4...

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Unformatted text preview: Chapter at Review 55 General Berrievv Guide: Chapter 4 ; Sequences and Summation I What isamethodtohelp ﬁndsneaplititfornnﬂaforasequencc whose ﬁrstfewtermsare given [presided a nice explicit formula existal)? (pi £01} I What is the summation notation for a sun: that is given in expanded form? fp. \$132} I What is the expanded form for a sum that is given in summation notation? (p. ME} I 'What is the product notation? (p. 905} o What is factorial notation? (p. sss) I What are some propa-ties of summations and products? (p. 33?} I How do you transform a summation h}? makinga change oftnriahle? (p. 209} 'I Whatisanaigorithmfor convertingfromhaaelﬂtohaseZ? rs. so} Mathematical Induction I Whatdoyoushnwlnthebasisstepandwhatdoyoushowinthe inductivestepwhmi you use {ordinary} mathematical induction to prove that a property involving an integer n is true for all integers mentor than or equal to some initial integer? {p 313) I What is the inductive hypothesis in a proof by [ordinary] mathematical induction? (p. 313} I Are you able to use {ordinary} mathematical induction to construct proofs involving various kinds of statements such as formulas, divisihility properties, and inequalities? (pp. 213, sec, 333, 339, 331, 232) I Areyoo abletoapplytheﬁbrtnnlaforthe sum oftheﬁrstn positive integers? (p. 292} I Areyon aisletoaraplyr theformtﬂaforthssnrn oftlresuooessive powersoi'amlmber, starting with the aeroth power? (p. 235) Ethan]: Mathewnatical Induction and The Well—Drdering Principle I What doyoushowinthe basisstepanri what doyoushowintheindnctive step when pounce strongmathemﬁical induction topmvethatapropertyinvolvinganintegernis trueiorall integers greater than or equal to same initial integer? (p. 335) I What is the inductive hypothesis in a. proof by strong mathematical induction? (p. 335} I Are you able to use strong mathematical induction to construct proofs ofvarions statements? (pp. 335-340) I What is the well—ordering principle for the integers? (p. 215') I Are you able to use the well-ordering principle for the integers to prove statements. such as the existence part of the quotient-remainder theorem? (p. 241) I How are ordinal-3,r mathematical induction, strong mathematical induction, and the well- metering principle related? (1:. £13} ‘thm Correctness I What are the ore-condition and the posbeondition for an algorithm? (p. 245} I What does it mean Em: a loop to be correct with respect to its on.L and post-conditions? (p. 345} I Whatisaloo-pinvaﬂant? (p. are) I Howdovon nsethe loop invariant theorem toprovethntaloopis oorrectwith respectto its pre- and post-mnditioas? (pp. Sid-£53} ...
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