Quiz 2 Solution•Prove that For all integersa,b, andcifa|b,and a∤c, thena∤(b+c)••2
Sample Exam Problems•1-Prove or disprove sum of two positiveirrational numbers is irrational•2- prove that there exists a unique primenumber of the formn2+2n-3 wherenispositive integer.•3- Prove that for all integersaif a3is eventhen a is even.5
Finding Terms of Sequences Given by ExplicitFormulasDefine sequencesa1,a2,a3,… andb2,b3,b4,…by the following explicit formulas:Compute the first five terms of both sequences.Solution:
Product NotationA recursive definition for the product notationis the following: Ifmis any integer, then
ExampleCompute the following products:a.b.Solution:a.b.
Properties of Summations and Products
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Numerical digit,Positional notation,Decimal,Rational number,Numeral system