For which equality in the following calculation does the induction hypothesis get used? 1. k+1) (2(k+1) – 1) i=1 (E (2k – 1)) + (2(k+1) – 1)

Q: (5) 7(3k – 1)² +26(3k – 1)–8

A: On simplifying the above expression,we get

Q: Find the value of c if -226 Σ1+0 2 C = No decimal entries allowed.

A: summation (1+c)^-n from 2 to infinity converges only if |1+c|<1(1+c)^-n is a GP series. Use the…

Q: Find the Cholesky factorization A-[-+-+4] -1 20) A =

A:

Q: B2. Using induction, Prove that 2+ 6+ 10 + ..-+ (4n – 2) = 2n² for all n e N. B3. Simplify the…

A: Mathematical induction is one of the basic proof techniques. When a statement is valid for all…

Q: Consider the statement P(n) : 2n + 1 = 3 and P(k) is true so that 2(k + 1) + 1 = 2k + 2 + 1 < 2k + 2…

A:

Q: Q:- Show thet B(n, n) B( n+on+=2 1-40

A: The solution is given as

Q: Σ1 (3)* (?)² i=1 ►Give a combinatorial proof of the following identity (3η) = (²n) HINT: Remember…

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Q: 1. Using (2n +1)Pn= Pn+1-P-1: prove that P(x) = (2n-1) Pn-1(x) + (2n-5) Pn-2+(2n-9) Pn-3+.... - and…

A: Given : 2n+1Pn=Pn+1'-Pn-1' To Prove : (a) Pn'x=2n-1Pn-1x+2n-5Pn-2+2n-9Pn-3+ . . . . . .…

Q: use gauss's trick to determine R(n)=2+3+4+...+(n-1)+n+(n+1)

A: It is known that sum of first n numbers is n(n+1)2  that is  1+2+3+----+n=n(n+1)2 Gauss trick method…

Q: Express (2ay + 2x – 1) – i (a2 – y? – 2y) as polynomial in the binomial argument z = x + iy. iz + 2z…

A: Solution

Q: Find n if 2P(n, 2) + 50 = P(2n, 2) note: P(n, k) = nPk

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Q: 4n2 +14n +1 c. Let P(n):9+13+...+(4n+5) = Show P(k) P(k+1). Is P(n) true Vintegersn21? 10 Fon the…

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Q: For each integer n2 2, let P(n) be the following equation (n – 1)n(2n + 5) (i – 1)(i + 1) = 72 - 6…

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Q: (Vn)(n2 +n+ 17 is prime)

A: Since, you have posted multiple questions , I am doing the very question (ques 7)  according to our…

Q: (2) Give a proof by induction of the formula: P(n): 12 +22 + ...+ n² = "(n+ 1)(2n + 1) 6

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Q: 2. Find (w + 1)(w-w+1).

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Q: Select all of the following that are equivalent to >(2) +> (3k + 1)? k=0 k=0 п+1 A. O) (3k + 3) k=0…

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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: 4n² +14n+1 = Let P(n):9+13+...+(4n+5) 2 Show P(k)→ P(k+1). Does this mean P(n) is true Vintegers n ≥…

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Q: 4. Show that P(n,k)= P(n – 1, k)+ k · P(n – 1,k – 1). Using Combinatorial Proof.

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Q: Show that (m) (2n 4n n

A: As n → ∞, By Striling approximation formula n! tends to  sqrt(2 pie n) (n/e)^n

Q: Use Gauss's trick to determine H(n)=1+5+9+13+...(4n-7)+(4n-3)+(4n+1) I got n(4n+2)/2 is this…

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Q: 1 1 1 +...+ 1 lg 35 5g (2n– 1)(2n+1) 2n+1"<!

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Q: 34. a. 5(t – 4) + 2> 3(t + 1) – 3 or 2t – 6> 3(t – 4) – 2 b. 5(t – 4) + 2> 3(t + 1) – 3 and 2t – 6>…

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Q: k-1 S₁=Σa+id=(2a+(k−1)d) i=0 Prove this using induction.

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Q: Show that if A and B are both n × n, then (a) det(AT BT ) = det(A) det(BT ); (b) det(AT BT ) =…

A: Given A and B are n×n matrix.

Q: 82-28+3 92. Find (a) -1{ (8-1)2 (8 + 1)

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Q: Given p(x) = x + 4x²-3x+2 and =x +5x +2 R4. P(x) X-1 Which statement is true? Select all that apply.…

A: Topic:- algebra

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.