Question 3. In parts (a) - (c), prove that for all n ɛ N: (a) n-1 £(:)-I- n k k=1 k=0 (b) £(:)-- n = 2n+1 k k=0 (c) E(-1)* ( : ) = 0 k k=0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 10E
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Question 3.
In parts (a) - (c), prove that for all n ɛ N:
(a)
2(:)-2-
n-1
Σ
k
k=1
k=0
(b)
¿(:)--
n
Σ
= 2"+1
k
k=0
(c)
E-1* ( ):
n
= 0
k
k=0
(d) Prove that 2" + 3" is a multiple of 5 for all odd n E N.
Transcribed Image Text:Question 3. In parts (a) - (c), prove that for all n ɛ N: (a) 2(:)-2- n-1 Σ k k=1 k=0 (b) ¿(:)-- n Σ = 2"+1 k k=0 (c) E-1* ( ): n = 0 k k=0 (d) Prove that 2" + 3" is a multiple of 5 for all odd n E N.
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