The generating function of a_{n+1}=8a_{n}+4n*, where a,=3 is a. Σ2x)^k+Σ (4x) ^{k Ο b. Σ( 2x) ^{k}+ 2Σ (4x) ^{k Ο c. 1/2(Σ (2x) ^{k}+ Σ (4x) ^[K) Ο d.2Σ(2x)^{k)+ 2 Σ (4x) ^[k)

Q: Let yk = k", where n is a positive integer; then Ak" = (k + 1)" – k" - (1.112) nk"-+ n kn-2 +...+ 2.…

A: We have to solve given problem:

Q: Consider the generating functions a(z) = 1 + 2z+3z² +42³ +52 + = Σ(i+1)zi = i20 b(z) = 1+z+z²+z³…

A: We have to find a formula for the coefficient of zk in  (ab)(z), where  a(z) =…

Q: (3) Prove that n=2²°² is a square. 2K+1 where K = 1 $ (n)

A: This follows from the definition of euler Phi function

Q: [In (a* + 3) – In (2r* –- 1)] In (2r³ – 1) 7. lim

A: Definition used -             Limit of a rational function -             If limit x tends…

Q: Which of the following graphs is the slope field for d 11 || \-|-~ \ || | | \-2+- \\ -37-11 -3 -2 -1…

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Q: (1+v2)+i_ Z2 (1+2) (b) Show that -i 2

A:

Q: Problem 3. Let a, b and n be positive integers. Prove that (a) gcd(an, b″) = gcd(a, b)” and lcm(a”,…

A: To prove the given statements, we will use the following properties of the greatest common divisor…

Q: 21) f(x)=47x A) (4 ln 7)47x Write summation notation for B) (7ln 4)47x x(In 2) C) (In 4) 47x x(In x)…

A: Finding the derivative of f(x)

Q: 54. (р^ (~(~рv @)) V (р^@) %3р

A:

Q: fes Find the values of Sup(A), inf(A) and if possible those max (A) min (A) of a) A = √n²+²0+² / no…

A: To find the sup(A) and inf(A) and Max and Min of A if exists . As per the rule I am supposed to…

Q: 19) Find [sin( x9+ 9x) ]' = _by Chain Rule A) 9x8sin ( x9+ 9x) C) 9(x8+1) cos x 19) B) -9 x sin (…

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