7. Prove that if a, = 1, a1 = 4, and a, = 6a,-1 – 9an-2 for n > 2, then a, = 3"-(3 + n) for all n 2 0. Show all your algebraic steps! Basic case(s): Inductive Hypothesis: Inductive step - we need to prove:

Q: X4 X6 x8 x10 3. Y = x2 + 3! N Terms ** * ... 5! 16 1L +

A: Please rate and feel free to ask any query

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Q: 3 21. (k +1) k=1

A: The given expression is, ∑k=13(k2+1) To find the sum of the expression from k=1 to k=3 substitute…

Q: (n-1)! Use Euler's theorem to prove that if n is an odd integer, then n divides 2 -1.

A: Using Euler theorem to prove it.

Q: 5) Evaluate the expressions below if K(s) = 3s² - s+6. a) K(s+2) b) K(s) +2

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A: Given that  Number of people shake hands each other=25 To find  Number of shake hands will occur.

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

A: The solution is given as

Q: (a) 1,2, ..., 16, i.e. such that the sum of all numbers in each row, each column and each diagonal…

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Q: {21} s² +4 9-1 3 (28+5)³ 2} ₁-55

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Q: 4. Knowing that 1 + 3 + 5 + …+ (2n – 1) = n², find 1++3 +5 + .…+ 135 =

A: Solution :   Given that  1 + 3 + 5 + ... + (2n - 1) = n2    -----(1)

Q: Find the dual of the Boolean expression O T. (T+0). (+y+2) O a. (1.1). (* + y | 2) None of these OT.…

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Q: 2. Determine the following sets: a) {r €R: (3n EN\{0}) 2n – 1 < nx < 7n - 2} b) {r ER: (Vn EN\{0})…

A: An interval is nothing but a subset of the set of real numbers. When the two endpoints are included…

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Q: * :The nth term formula for { 1,0,1,0,... } is 1-(-1)" 2. an = A₂ = An خيار 2 1 + (−1)" 2.

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Q: Below is an incomplete proof Prove that 3n2 > 2(n+1)2 for n ≥ 5 3n2 > 2(n+1)2 Is equivalent to 3n2 >…

A: The question already shows how the proof for 3n2 &gt; 2(n+1)2 for n≥5 is equivalent to showing n2…

Q: 20232023 then how many 2 If x² - y² = 2023 pair of x,y where x, y ≤ N

A: We can factorize the given equation using the difference of squares formula: x2 - y2 = (x + y)(x -…

Q: Of the statements below, three are false and one is true. Find two of the false statements and give…

A: We will find counterexamples for the statements which are false.

Q: 10.The first three terms in the expansion of (1+x – 3x-)* are the same as the first three terms in…

A: Answer of Question #11 is not match with given option.please check it carefully...

Q: all n N we have We apply this successively for n = bn+1 bn N, N+1, n 9 bN+1 < (m + €)bN bN+2 < (m+…

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Q: 1. Show for all natural numbers n that (2k – 1) = 1+3+ ...+ (2n – 1) = n². k=1

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Q: Part 1. Obtain a solution to the following differential equation valid near the origin: 1.] For the…

A: Part 1. Given equation is y''+3xy'+7y=0   4. To Find: The recurrence relation for n≥2   5. To Find:…

Q: Solve for n in permutation 9(n²-1Ps) + 9(7²P6) = n²+1 P7 %3D

A: Let's find.

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Q: 3 - 4 fX = the value of X" is - 1 %3D

A: We have to find the value of X^n

Q: 7. (a) Prove that m³ + 2n² = 36 has no solution in positive integers. (b) Prove that for every n e…

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