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a 1 In parts (a) - (c), prove that for all n E N: (a) n-1 k k=0 (b) ¿(:)-- 2n+1 k k-0 (c) E(-1)* k=0 (:)-- = 0 k (d) Prove that 2" + 3" is a multiple of 5 for all odd n E N.

a 1 In parts (a) - (c), prove that for all n E N: (a) n-1 k k=0 (b) ¿(:)-- 2n+1 k k-0 (c) E(-1)* k=0 (:)-- = 0 k (d) Prove that 2" + 3" is a multiple of 5 for all odd n E N.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 51RE
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least element. 1 In parts (a) - (c), prove that for all n E N: (a) n-1 ¿(:)-Ë- k k=1 k=0 (b) in = 2"+1 k k=0 (c) in E(-1)* ( = 0 k=0 (d) Prove that 2" + 3" is a multiple of 5 for all odd n E N. (a) Given a surjective function f: [-1,1] → [-1, 1], prove or disprove: f-(f{0}) = (0}. (b) Find f(E) and f-'(E) for the function f (x) = log (x2 – 2x + 1) if E = (0, 3].
Transcribed Image Text:least element. 1 In parts (a) - (c), prove that for all n E N: (a) n-1 ¿(:)-Ë- k k=1 k=0 (b) in = 2"+1 k k=0 (c) in E(-1)* ( = 0 k=0 (d) Prove that 2" + 3" is a multiple of 5 for all odd n E N. (a) Given a surjective function f: [-1,1] → [-1, 1], prove or disprove: f-(f{0}) = (0}. (b) Find f(E) and f-'(E) for the function f (x) = log (x2 – 2x + 1) if E = (0, 3].
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