Use the PMI to prove that 3-1 is even for all n E N.

Q: Solve the following oblique triangle using the Law of Sines. Show your work! Round 1 place after the…

A: We are provided with following information : B=47.2o , C=73.7o b=56.9 ft According to Sine rule , we…

Q: Suppose we have o(n)= = 2 . What can you say about n?

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Q: Show that if x > 9, then x³ – 8x? + 2x > 3. Show that for all n e N, if n > 10, then nª – 2n² > 3n³.

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Q: • G= *-3 ) • G = , det (G) = 10 %3D 4] Then x=12 O A) TRUE O B) FALSE

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Q: P(X₁ = x₁, ..., Xn = xn) = P(X₁ = x₁) [I²²2 P(X; = Xi| X₁ = X₁, ..., Xi−1 = Xi−1 )

A: Here we have a given equation that

Q: Verify by o Mathematical Induction dt todt E (2-1) = n²(2n²-1) for alt nz!

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Q: Fix a € (0, 1). Determine inf(B) for B = {an: ne N}. You can just give your answer for this part…

A: We have to find the  for

Q: Given that m*n=3m-n, find the value for y for which (2*1)*y=0

A: Given mn=3m-n

Q: Suppose n E Z. Prove that if n is even, then n2 + 5n + 4 is even.

A: Note: We know that the square of an even number is always an even number, since  Let x is an even…

Q: n° Prove that =n² + o(n). n² – 1

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Q: The small positive integer n for which (1+i)=(1-1)" is =. ........ 8 4 12

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Q: N-1 N, k-r = mN, m an integer | Se-i(27/N)(k-r)n n=0 0, otherwise

A: To prove: ∑n=0N-1e-j2πNk-rn=N,k-r=mN, m is an integer0,otherwise

Q: Let m, n 1 be integers. We have

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Q: 10. Show that È k(C) = n2"-1. Using Combinatorial Proof. k=1

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Q: n (n + () A k=0 | B, = 0.

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Q: Prove that : L²₁ (1-x²) Pm Phd x T 0. 2n (n + 1) 2n + 1 4 mn. m = 11. m, ne N

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Q: PLS HELP ASAP ON ALL ASKED QUESTIONS PLS

A: Ans 1: (d) Degree of polynomial is 6Ans 2 : (b) Function changes its sign at x =…

Q: (d) For which e E {0, 1, ..., 9), is 12e128 divisible by 8? Find all such e. 1

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Q: Prove n (2k – 1) = n² - k=1 for every n EN.

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Q: 42. Let e = 1+ 1/1! + 1/2! + 1/3! + Show that if k is a positive integer, then kle is not an…

A: Given , e=1+11!+12!+13!+....we need to prove if k is a positive integerthen k!e is not an integer

Q: (-1)^ xIn lIt) = (-1)" (n+ 2 2n+1(n + 1) che exact value of

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Q: (1.2) Show that m m+n+1] m k=0 for any two positive integers m and n.

A: Please check the next step for detailed answer.

Q: ind all solutions for n EN for which P(n, 4) = 12P(n, 2).

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Q: Indicate the smallest integer n such that (6x²+4x)³ f(x) = € 0(x¹). 2A-4x On=4 O n=2 O n=1 O n=6 O…

A: f(x) = (6x2 + 4x)3/(x4 - 4x)         = {2x(3x + 2)}3/{x(x3 - 4)}        = 8x3(3x + 2)3/{x(x3 - 4)}…

Q: Show the solution that a,+1 < a, for each n E N (-1)" п! n=1

A: Find your answer below

Q: . Use Mathematical Induction to show that for all n > 1. 71 i=1 F2i = F2n11-1

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Q: (b) The integer n is even if and only if (n +1)2-1 is ev

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Q: If k = (0.0003,-0.0012, 0.0015,-0.0014) in R4 then -5.2||||=0.0062

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Q: Let S₁ = {1-(-1)/n:ne N}. Find inf S, and sup S..

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Q: Show that for any n E N, n(n + 1)(2n + 1) k=0

A: The solution is given as

Q: n(n+1) For all n E N, prove 1 + 2 + ··· + n = 2

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Q: (3x* – 1) dx + x°dy = 0; when x = 1, y = 1

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Q: (2) Prove that (1+x)" > 1+nx for all x > 0 and n > 1.

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Q: Find the derivative using the methods of Example 6 in the text. y = x8x y =

A: Consider the equation y=x8x We have to find the derivative of y=x8x Taking logarithmic both the…

Q: Show that for all n e Z, n? – 3n +17 2. -

A: Given: For all n∈ℤ, n2-3n+1≠2