n Use induction to prove: for any integer n 1, (6j 4) = 3n...

Transcribed Image Text:

n Use induction to prove: for any integer n ≥ 1, Σ(6j − 4) = 3n² — n. - j=1 Base case n = Inductive step Σ(6j - 4) = ₁, 3n² Assume that for any k ≥, Σ (6j – 4) = we will prove that (6j – 4) = WI (6j − 4) = Σ(6j − 4)+| FO = = = 3 + -n= + k+ ²+k+) − (k+1) -(k+1) k.² By inductive hypothesis η Use induction to prove: for any integer n > 0, Σ2.3 = 3*+1 – 1. — j=0 Base case η Σ2.3 = C 3n+1 Inductive step Assume that for any k > Σ2.3 we will prove that Σ2.30 - = Σ2.3 - Σ2.3+ j=1 j= = 3. -1= + ΣΟ Ο By inductive hypothesis n Use induction to prove: for any integer n ≥ 1, Σ(6j − 4) = 3n² — n. - j=1 Base case n = Inductive step Σ(6j - 4) = ₁, 3n² Assume that for any k ≥, Σ (6j – 4) = we will prove that (6j – 4) = WI (6j − 4) = Σ(6j − 4)+| FO = = = 3 + -n= + k+ ²+k+) − (k+1) -(k+1) k.² By inductive hypothesis η Use induction to prove: for any integer n > 0, Σ2.3 = 3*+1 – 1. — j=0 Base case η Σ2.3 = C 3n+1 Inductive step Assume that for any k > Σ2.3 we will prove that Σ2.30 - = Σ2.3 - Σ2.3+ j=1 j= = 3. -1= + ΣΟ Ο By inductive hypothesis

Answer rating: 100% (QA)

Date1 To prove For ny 1 Base case A 2 6f4 6j4 61 Y 64 11 87 n 11 4 pr... View the full answer