Use induction on n to show that η k=1 k4 = 15 5 η + 1 η* + 2 1 3 3 1 ·η. 30

Q: what is the generating function of an  an+1=4an-an-1 (n>2)  a0=1, a1=1, a2=4

A: We have been given a recurrence relation . an+1=4an-an-1 , a0=1 , a1=1,a2=4  For , homogenous…

Q: Determine one real root of 2xcos2x – (x – 2) = 0 cn the interval (2, 3)using the Regula-Falsi…

A: Given 2x(cos(2x)) - (x-2)2 = 0  Let f(x)=-(x-2)2 + 2x(cos(2x)

Q: 2. Find all possible expansions of f (z) = 7(2²-9) 1 about z=1.

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Q: Determine the z-transform of the sequence x(n) = 3"u(n – 3) using z-transform properties. Express…

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Q: The z-transform of x(n) is X(z) = 1 + 2z-1. Find the z-transform of (1/2)^x(n − 2). a. 0.33(z-²-z-³)…

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Q: Prove that Σan σ(d) φ (n/d) nτ (n) and ΣIn τ(α)φ(n/d) σ(n). ||

A: As per the question we are given two sum identities including the Dirichlet convolution :…

Q: The residues of * ƒ(z) = O 4/9,-4/9 O-4/9, 4/9 O 4/7,-4/7 4z (z − 1)(z + 2)² -4/9, -4/9 O 4/9.4/9

A: The given problem is to find the residues of the given complex function at the obtained poles.

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: 4. Show that the Fourier series for the periodic function of period 2 defined by -{₁ f(0) = is given…

A: Given: fθ=0,when -π<θ<0sinθ,when 0<θ<π We have to show that the Fourier series of the…

Q: Prove that : Σ j=1 m=1 2.

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Q: 1. Given the function: f(x) = x + n, -n < x < n a. Plot the graph de -4n <x < 4n b. Find the Fourier…

A: Given that fx=x+π,−π&lt;x&lt;π To plot the graph over the interval -4π&lt;x&lt;π. To calculate the…

Q: Question 6 Use the substitution method to compute 9r e d. -- + K.

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Q: Verify that the sequence Un(x) = cos ( (n + n ɛ N form an orthogonal set of functions on [0,1]. That…

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Q: The DNA molecule comes in the form of a double helix, meaning two helices that wrap around one…

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Q: (Numerical Analysis) The value of Euler's number, e, can be approximated by using this formula: e…

A: #include &lt;iostream&gt;#include &lt;iomanip&gt;#include &lt;cmath&gt; using namespace std;

Q: Prove that (n – 1) +n° + (n + 1)° is divisible by 9 for n E {1,2,3, . }

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Q: Show

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Q: 4. Use mathematical induction to prove that Vn E Z* u {0}, []²=o(2i + 1)! > ((n + 1)!)**. n+1

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Q: 3) For a periodic signal x[n] with Fourier series coefficients a, following information is given: i.…

A: The properties for a periodic signal xn : ak=-ak-4 x2n+1=-1n Period=8 If xn is a signal then the…

Q: The z-transform of x(n) is X(z) = 1 + 2z1, /z/# 0. Find the z-transform of the following sequences.…

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Q: Prove that (a) P(En F) = P(E)- P(En F) (b) P(EnF) =1-P(E) – P(F) + P(En F)

A: Solution: 6. Here, it is needed to prove that

Q: 3. Let h: Z→ Z be the function h(r) = = x mod 4. Find h-¹(0), h-¹({0, 1, 2, 3}), and h-¹(4). Explain…

A: In this question we can easily observe that that output of the function is the remainder when any…

Q: 2. Define the function a(n) as follows: n = 1 n = 2 2a(n-1) + a(n − 2) n ≥ 3 5 a(n) = 10 and let…

A: Given that a1=5, a2=10, an=2an-1+an-2, for n≥3 Our aim is to prove that an&lt;3n for n≥3 using the…

Q: an -1 = IT 11 n'll 38 | 1.9x-nnnx XY [ 30 ] | 5 5n¹ + 5.8 (11) corn (11) n² 3.8 COINIT (cornx)

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Q: Suppose A E C such that X(2+i, 3 – i) = (5- i, 7- 5i). Then (1) A = (1– i) (2) A = (2– i) (3) Does…

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Q: The z-transform of x(n) is X(z) = 1 + 2z¹, /z/# 0. Find the z-transform of the following sequences.…

A: The z-transform of x(n) is X(z)=1+2z-1, |z|≠0. The given sequences are:…

Q: on 3. Let f(x) = |x| Compute f(n) for all

A: Given:  f(x)=x x∈-π,π. To find: a) f(n) for all n∈ℤ.              b) ∑n=1∞12n+14 and  ∑n=1∞1n4

Q: We are given A e R™** and its inverse A- E R"X: [11 2 22 2 1 1 2 22 11 2 2-2 2-3 2n-4 .... 1 -1 -1 1…

A: Condition number: The condition number of a matrix is given by, κ(A) = A∞A-1∞. Norm of matrix: The…

Q: 1.5 Prove that |e=2=| 0.

A: We need to prove that |e-2z|&lt;1 if and only if Re(z)&gt;0 The solution is detailed below.

Q: The function f(n) = 2", n = 1, 2, 3,... %3D %3D The function f(n) = n!, n 0, 1,2,... %3D The…

A: The recursive definition of a sequence is a general formula that describes the relationship between…

Q: Determine a and b such that p(x) = x² + ax + b satisfies p(1) = 0 and p'(1) = 9. (Give an exact…

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Q: 4. Prove the formula below using mathematical induction n nº + n log 2* : ") log 2 2 k=1

A: Use mathematical induction to prove the given equation. Let n=1LHS:log 21=log 2RHS:1+12log 2=log…

Q: ex:-Find The Fourier expansion ot FOX=X-x³ -1<x<!

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Q: 8. Prove the following. A. Let X = {a e N|a = 3t + 4, for some t e N} and Y= {a eN | a = 21t + 4,…

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