In the following C denotes the set of complex numbers with i = V-1 and No...
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In the following C denotes the set of complex numbers with i = V-1 and No = {0, 1, 2,3..}. If z € C and k e No, then z(z-1)-(3-k+1) if k>0, () { if k = 0. is called a binomial coefficient to be read as 'z choose k'. a) Find (), (), (). b) Let z € C. Prove that 2 - k k+1k for all k E No. c) If z € C, prove that (':)- () • (* : ) - (:) %3D k +1 k+1 for all k E No. d) Prove the binomial formula. If z, w e C, then (z + w)" = E(") k=0 for all n e N. e) Is the binomial formula also true if n 0? [6,6,6,6,1] Question 2: a) Prove that the set Z of the integers is not bounded above and not bounded below. In the following C denotes the set of complex numbers with i = V-1 and No = {0, 1, 2,3..}. If z € C and k e No, then z(z-1)-(3-k+1) if k>0, () { if k = 0. is called a binomial coefficient to be read as 'z choose k'. a) Find (), (), (). b) Let z € C. Prove that 2 - k k+1k for all k E No. c) If z € C, prove that (':)- () • (* : ) - (:) %3D k +1 k+1 for all k E No. d) Prove the binomial formula. If z, w e C, then (z + w)" = E(") k=0 for all n e N. e) Is the binomial formula also true if n 0? [6,6,6,6,1] Question 2: a) Prove that the set Z of the integers is not bounded above and not bounded below.
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Related Book For
Intermediate Accounting
ISBN: 978-0077400163
6th edition
Authors: J. David Spiceland, James Sepe, Mark Nelson
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