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 . The sequence {g} is defined recursively as follows:n80=1 andad 8 n = 3.8₁If the theorem below is proven by induction, what must be established in the inductive step?(A)5Theorem: For any non-negative integer n, g = 2" - n-.n2BⒸ(D)then gFor k ≥ 0, if g = 3·8 k-1 +2k,53= — . 2k +¹ − (k + 1) - 2/22k+1n-1then g+2₁, for n ≥ 1.n5For k ≥ 0, if g,20-2¹4-kk+1then gk+1-k-For k ≥ 0, if g = 3 ⋅8k_₁+2k,kk-153k+1= -√2₁ 2² + 1 - (K + 1) - 12/2= 3.g₁ +2(k+1).k5For k ≥ 0, if għ =2322k - k-then 8 = 3.3.8 +2(k+1).k+13232.

The principle of induction states that at inductive step to prove a statement P(n), we need to prove…

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 .

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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