Use induction to prove: for any integer n ≥ 1,(6-4)= 3n² - n. Base case n = Inductive step Assume that for any k > k+1 Σ(6-4)= (6j - 4)+ j=1 j=1 = Σ(6; – 4) = j=1 = =( = 3 k² + k² + k+ k+ j=1 j=1 ,3n²-n= (6-4)= )-(k+ 1) -(k+ 1) k+1 , we will prove that (6-4)= j=1 By inductive hypothesis

Q: 2) Find the expression for F(z) while solving the recurrence relation 2yk+2 - 3yk+1 +7yk = kak by…

A: Given: Let us consider this as equation (i) 2yk+2 -3yk+1+7yk = kak

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A: Here we have a given equation that

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Q: n(n + 1)(2n + 1) 2. Use induction to prove that )k2 for all n e Z+. %3D 6. k=1

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A: Consider S=32+82+132+ . . . .+15n-22

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A: See the answer below

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Q: Solve the recurrence relation using the generating function technique. b0=1/2 bn=3bn-1 - 1/2…

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Q: 7

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Q: Let ao = 0, a₁ = 6, and an Use the PCI to prove that an = 7 - 1 for all n E w. = 8an-17an-2 for all…

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Q: nductio

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Q: Σ s2 an convergent or divergent?

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A: Since you have posted multiple questions and we can answer one question at a time. So, answered…

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A: To prove:We will use mathematical induction to prove this.Let

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Q: Use proof by induction to prove that: =-n°(n+ 1)? %3D r=1

A: Mathemetical Induction

Q: n (3n–1) 2 B. Use mathematical induction to prove that P(n): 1+4+7+..+(3n-2) = n2 1. Use the first 2…

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Q: In the inductive step, we assume that for any k > 10 , P(j) is true for any 8 <js (k-2) and we will…

A: The proof by mathematical induction consists of two steps: The proof consists of two steps: The…