ised. (a) Ž 3n2+1 5n2+3 n=1

Q: 8. 2n+1

A: We will solve the problem using root test.

Q: The number of nonnegative integer solutions to the equation ₁ + x₂ + x3 + x4 Oa. (3) Ob. (²) C. none…

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Q: 1+ x Σ Aa" (1 – 2)? n=0

A:

Q: Determine O a. O b. dy d. (4r+3) (4r² +6r+3) r(r+1)(r+2) (4r+3) (4r²+6r+3) r(r+1)(r+2) r(r+1)(r+2)…

A:

Q: (-i)a is e(1+4n)i wheren is an integer. where n is an integer. O equal to the above O equal to the…

A: Any complex number, z can be written in the form of  z=reiθ . The complex number i can be written as…

Q: Does each of the following series converge or diverge? Why? Show all your work and MUST include the…

A: The objective of the question is to determine whether the given series converges or diverges. The…

Q: (2n)! – (2n + 1)! (2n)!

A: It is required to find out , 2n! - 2n+1!2n!  For this we use factorial properties.

Q: Find the convolution of (a) 2tu(t) and t³u(t) (b) eu(t) and tu(t) (c) e2tu(t) and etu(t). Answers 1.…

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Q: So an = n 16 n+ 16 (n-1) 16 (n-1) + 16 = n - 16 n+ 16 I X 11 (n + 15) (n + 16)

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Q: Differentiate f (x) = 71n(x²-6x+3) A. (2x – 6) 7ln(x²-6x+3) f' (x) = x2 – 6x + 3 - В. In(7) (2x – 6)…

A: Given query is to find the derivative of the expression.

Q: (2n)2k B2k 3(2k) = (-1)k-1 2(2k!)

A: We will use the knowledge of basic theory concerning the Riemann zeta function and the Bernoulli…

Q: (d) (n-r+1)! (n - r - 1)! *

A: According to the given information in this questionwe need to simplify the given form

Q: n Find I (1) n=2

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Q: For which value of b is the equation 2n+1 11 5n+1 10 satisfied, n=1 where b>2 ? (a) b=3 (b) b=4 (c)…

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Q: h(n) = 4n – 1 g (n) = n² - n Find (h o g) (4n)

A: Consider the functions  h(n)=4n-1g(n)=n2-n

Q: (-1)n+13n (b) n5n n=1

A:

Q: a. b. INGIN IN C. + S (S-1)² e35 + 5-1 e-3s S 5+1 d. None of the above L{2+ (t-3)et-3 U(t-3)] = +

A: Consider:  L2+t-3et-3 Ut-3=L2+Lt-3et-3 Ut-3 Now, L2=2L1=2×1s                      since L1=2s So,…

Q: If S(8f(x)+ 5) dr = 8 , then

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Q: 4 Σ n2 +4n +3 - 9-n+24n+1

A: Separate the sum.

Q: Make n the subject of the equation s=n/2 (2a+(n-1)d)

A:

Q: 10 (S) (S+3)² = (3) (S+3) ²³ + K₂ (S+3) + K3+ K₁ (3+3)

A: The given equation is 10ss+32=k1ss+32+k2s+2s+32+k3+k4s+3 To find the value of k3 when s=-3 .   The…

Q: (A) I = and (B )I = . Find 2A D - BD O O O none of the above

A:

Q: (a) Show that for n> 1 we have F2 = FnFn+1 − FnFn-1. (b) Use part (a) to show that F² + F² + . + F²…

A: Fn denote the Fibonacci sequence, satisfies Fn+1=Fn+Fn-1.              n≥2 And         F1=0,…

Q: Find L-

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Q: nv n=1

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Q: hich of the following expressions are equivalent to 2n 4n2 + 4n n+ 5 4n2 + 6n 10 (n+ 1) C 4n (n+1)…

A: given,

Q: P= +-1 Q=1 ++1 P(ar) =

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Q: 2 + 4 + 6+ . . . + 2n = n(n + 1)

A: On solving this we will get

Q: 8 For which values of mis x - 1 a factor of x³ + m²x² + 3mx + 1? (a) Show that n = 1 is a root of…

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Q: Compute the Convolution of the following pairs of discrete time signals. x[n] = (u[n + 2] – u[n –…

A:

Q: (c) n=1 n² + 5

A: The objective of the question is to determine whether the given series converges or diverges. The…

Q: Find L(3t + 13]. + 13 s2 13 (8-1)2 13 2 + 13

A:

Q: Select all of the following that are equivalent to >(2) +> (3k + 1)? k=0 k=0 п+1 A. O) (3k + 3) k=0…

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Q: What is the zero of r (x) x +12 ? %3D O12 O 9/3 O None of the above /3

A: We put polynomial equal to 0 and find out the value of x. The value of x is our zero of r(x).

Q: (b) 6 + 7 + 8 + 9 + ... + k

A: (b) Given that 6+7+8+9+...+k The objective is to find the sum. The formula for sum of numbers are,…

Q: р-1 E (3k? – 2k + 1). k=-2

A: we have, ∑k=-2p-1(3k2-2k+1)

Q: Ex if A = [2 - 1], then find P(1) if P(x) = x²-3x² + 2x-5 0 @ P(x) = 2X²³-4x²=7X-6 Find A¹ if 3…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: If x is N(0,2) find (a) P{1£x£2} and (b) P{1£x£2x³1}

A: Given that,  X~ N(0,2)  Where, mean of x= 0  Standard deviation of x= 2 We know that, z-score=…