1 Show that -2 logn diverges to . ∞ n=2 1 Prove that Σn(n+1) = 1. (hint: n(n+1) = n n+1).

Q: n(n+1)(2n+1) 2.Prove k2 = for n > 1. 6. k=1

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Q: Expand f(x) = |sinx| in Fourier series. This function is definite for all x and represents a…

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Q: Solve this attachment.

A: We have to show ∑k=0n-1knk=0 using binomial theorem. We know by binomial  theorem…

Q: Suppose that 10 x (16 + x) = Σ Cnxh n=o Find Coefficients: Co= C₁ = C2= C3= C4 = Radiance of…

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Q: 2. Find the value of an(n + 0) in the Fourier series expansion of the functions f(x) = sin(Mx)…

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Q: 5. Determine if Σn=3 convergent. cos(NT) is absolutely convergent or conditionally n+1

A: "Absolute convergence" means a series will converge even when you take the absolute value of each…

Q: 5. Find the Fourier series of |x| of period 27 and evaluate the sum 1 1+ 32 1 +... 52

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Q: Let T(N) = 1. T(floor (N/3)) + 1 and 7(1) = T(2) Prove by induction that T(N) ≤ log N + 1 for all N…

A: Given: TN=TfloorN3+1 T1=T2=1   To Prove: TN≤log3N+1 for all N≥1, using induction.

Q: Use mathematical induction to prove that cos(x+n) = (-1)" cosx where n≥le J*.

A: Mathematical induction is defined as a mathematical technique that is used for the expression,…

Q: What is the complex Fourier series of the function f(t) = cos t? Hint: if you're confident, you can…

A: Given function is  ft=cost. We know that the Fourier series of a function can be written as:…

Q: Assume that the coefficients in the expansion f(x) = anx" n=0 satisfy Enanx" – E Anx"+1 = 0. n=1 n=0…

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Q: Show that >n"x" diverges for all x + 0. n=0

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Q: nd is it or diver Convergent (0.627 an %3D (3.15)"

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Show that {\/? sin(n – )(4)} is an orthonormal set in C(0,1). State condition(s) under which an…

A: 1) Given the sequence of functions ϕnx=2lsinn-12πx2 in the interval 0,l.   Formula:1) If…

Q: Which of the following are convergent or divergent? Show your work. 72 i. En=2 lnn ii. En=1 3 1+ Vn…

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Q: The following table gives a random discrete signal at a variable rate. 2n 2n 3 3 3 3 f(t) 1 1.40 1.9…

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Q: Find the Fourier series of the function of period 27 such that f(x) = |a| for %3D 1 1 1 -A <x < T.…

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Q: 1. Show that {/ sin(n – )()} is an orthonormal set in C(0,1). 2. State condition(s) under which an…

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Q: 100 8. Rewrite log2 II* П 24 as an expression involving summation notation. i=10

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Q: Pls solve this question correctly instantly in 5 min i will give

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Q: n In the interval (−л, π), ³₂ (x) : = √ : exp(-n²x²). (a) Expand &n (x) as a Fourier cosine series.…

A: As per the question we are given a function δn(x) and we have to : Expand δn(x) as a Fourier cosine…

Q: Determine if the given is convergent or divergent. (x²+1)² n Zn=1 (n²+1)²

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Q: 1/16 Perform a test to determine if tan (80)d0 converges. b lim tan(80)d0 b-x/ 16" 0 (Simplify your…

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Q: A coin is tossed repeatedly, and heads turns up with probability p on each toss. Let hn be the…

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Q: Solve for the moment generating function of X if for all natural number n, X ∼ U {1,2,…,n}.

A: Given that, X ∼ U {1,2,…,n} , we need to solve for the moment generating function of X if for all…

Q: 00 n + 1 is divergent. If we multiply any constant (labeled as h)to the n + 1 such that n + 2 n=1 n…

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Q: {fn(x)}1 converges a.e. to a function f(x) to be determined.

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Q: - 00 S 2 dx xx² (1 + e²*) (1+e³) -00 X convergent or divergent?

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Q: Find the appropriate Fourier cosine or sine series expansion for the function Decide whether the…

A: The given function is  Clearly, the  given function is an odd  function as Then, the fourier  series…

Q: Q(A). Let {fn(x)}-1 00 n%=D1 be a sequence of functions (1+ (x – 2)* S, - defined over [2,3]. Show…

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Q: n=1 n³ cos² n n²e²n + Inn

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Q: Prove that these two E E cos (Tin) não Inn 2 are تم 22=1 convergent (-1) h 22²41

A: A series is defined as the combination of the sequence. A series is said to be convergent when n…

Q: Show Recurrence that the solution to T (n) = T (2n/3) + 1 is Θ( log2 n)

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