Question 2.2 / Vraag 2.2 Prove, using mathematical induction, with all steps properly written down, that Vn E Z, n 2 0 Bewys met behulp van wiskundige induksie, met alle stappe behoorlik uitgeskryf, dat Vn E Z, n > 0 1 An = 1 2n

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Question 2. 1 Let ?0 = 0 and let, for ? = 0, 1, 2, ⋯, ??+1 = 1 + ?? / 2 Write down the first four terms of the sequence ?0, ?1, ?2, ?3, ⋯. Question 2. 2 Prove, using mathematical induction, with all steps properly written down, that ∀? ∈ ℤ, ? ≥ 0 ?? = 1 − 1/2 ^?
Question 2/ Vraag 2
[12]
Question 2.1 / Vraag 2.1
(4)
Let a, = 0 and let, for n = 0, 1, 2, ·…,
Laat ao
= 0 en laat, vir n = 0, 1, 2, ·…,
1+ an
аn+1
Write down the first four terms of the sequence ao, ɑ1, a2, ɑ3, *¨*.
Skryf die eerste vier terme van die ry a,, a1, a2, a3, •… neer.
Question 2.2 / Vraag 2.2
(8)
Prove, using mathematical induction, with all steps properly written down, that Vn E Z, n > 0
Bewys met behulp van wiskundige induksie, met alle stappe behoorlik uitgeskryf, dat
Vn E Z, n > 0
1
an
= 1
2n
Transcribed Image Text:Question 2/ Vraag 2 [12] Question 2.1 / Vraag 2.1 (4) Let a, = 0 and let, for n = 0, 1, 2, ·…, Laat ao = 0 en laat, vir n = 0, 1, 2, ·…, 1+ an аn+1 Write down the first four terms of the sequence ao, ɑ1, a2, ɑ3, *¨*. Skryf die eerste vier terme van die ry a,, a1, a2, a3, •… neer. Question 2.2 / Vraag 2.2 (8) Prove, using mathematical induction, with all steps properly written down, that Vn E Z, n > 0 Bewys met behulp van wiskundige induksie, met alle stappe behoorlik uitgeskryf, dat Vn E Z, n > 0 1 an = 1 2n
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