The sequence {g} is defined recursively as follows: n 80=1 and ad 8 n = 3.8₁ If the theorem below is proven by induction, what must be established in the inductive step? (A) 5 Theorem: For any non-negative integer n, g = 2" - n- . n 2 B Ⓒ (D) then g For k ≥ 0, if g = 3·8 k-1 +2k, 5 3 = — . 2k +¹ − (k + 1) - 2/2 2 k+1 n-1 then g +2₁, for n ≥ 1. n 5 For k ≥ 0, if g, 20-2¹4- k k+1 then g k+1 -k- For k ≥ 0, if g = 3 ⋅8k_₁+2k, k k-1 5 3 k+1 = -√2₁ 2² + 1 - (K + 1) - 12/2 = 3.g₁ +2(k+1). k 5 For k ≥ 0, if għ = 2 3 2 2k - k- then 8 = 3. 3.8 +2(k+1). k+1 3 2 3 2 .
The sequence {g} is defined recursively as follows: n 80=1 and ad 8 n = 3.8₁ If the theorem below is proven by induction, what must be established in the inductive step? (A) 5 Theorem: For any non-negative integer n, g = 2" - n- . n 2 B Ⓒ (D) then g For k ≥ 0, if g = 3·8 k-1 +2k, 5 3 = — . 2k +¹ − (k + 1) - 2/2 2 k+1 n-1 then g +2₁, for n ≥ 1. n 5 For k ≥ 0, if g, 20-2¹4- k k+1 then g k+1 -k- For k ≥ 0, if g = 3 ⋅8k_₁+2k, k k-1 5 3 k+1 = -√2₁ 2² + 1 - (K + 1) - 12/2 = 3.g₁ +2(k+1). k 5 For k ≥ 0, if għ = 2 3 2 2k - k- then 8 = 3. 3.8 +2(k+1). k+1 3 2 3 2 .
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 53E: Given the recursively defined sequence a1=0,a2=30, and an=8an115an2, use complete induction to prove...
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The sequence { g subscript n } is defined recursively as follows: g subscript 0 = 1, and g subscript n = 3 * g subscript n - 1 end subscript + 2 subscript n, for n greater or = than 1 .
If the theorem below is proven by induction, what must be established in the inductive step?
Theorem: For any non-negative integer n, g subscript n equals 5 over 2 times 2 to the power of n minus n minus 3 over 2 .
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