2" (a) 3 3n+1 (c) E(-1)"; 4n n=1 (b) 3+5n² (4) E n+ n2 n=1 n=1

Q: (п+2) Zn=3 (п+1)3 (-1)"п? Ln=1 n2+n+1 (-2)п Zn=1 n2 (-3)п Ln=0 (2n+1)! п10 Ln=1 (-10)п+1

A: (1).  The given series: ∑n=3∞ (n+2)(n+1)3

Q: 23 4- [fe** dycdx ans :(e' - e' )(e² – e') 12

A:

Q: Find for x³+y³ = 2. -4x O O (E) None of these ○ 3x² + 3y² = 0 2x *(*_*) O

A: Note:- As per the company guidelines we can solve first question. I hope that the given solution…

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Q: L(e-3t)= %3D 1 s2- 3 1 .bO s2+3 S-3 1 .dO s +3 1.

A: We can solve it by definition of Laplace method Consider Le-3t = ∫0∞e-ste-3tdt=∫0∞e-(s+3)tdt=…

Q: (-2)"+1 n+ 5" (2n)! 2n - n! - n (a) (b) (-1)". n=1 n=1 (c) E(-1)": (n!)'3" (2n + 1)! (d) 5 (-1)"…

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Q: (-1)"-1 5+ Vn 1. n=1 3 2. 1+νη n=1 5+ νη 1+ νη 3. n=D1 1 2η 4. 3+ νη n=D1 1 5. I (-1)°, (-1)*.

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Q: (x-4x² +7x–9 - dx x-3 A x3 * - 4x + 3 In Ix-3 I + C C x3 * + 4x + 3 In Ix-31 + C B x3 x? D x3 x? +…

A:

Q: TL ( - k) = | k-1 a. 6n + (n + 1)(2n + 1) - b. n(n + 1)(2n + 1) c(n²-1) C. O d. n3 e. 00 f. 플 (n +…

A:

Q: () 5 3 1. Solve the initial value problem ' 3 with (0) = 3 1 2

A: Given solve the initial valve problem, x→'=-5232-3212  with x→0=3-1

Q: n-1 n-1 k n-2 n-2 - = P k X6n-10 X6n-9 = 4 - n-1 п-1 n-1 h k k n-1 X'6n-8 = r X'6n-7 = P h - . k - 4…

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Q: How does h(n) = n2 / 2n behave for large whole-number values of n? Does h(n) tend to infinity?

A: Consider the function:      hn=n22n Determine end behavior for the large whole number value of n.

Q: Solve for k: ln(k − 3) + ln(k − 2) = ln (2k + 24

A:

Q: E1 (arctan(2n+1) – arctan(2n – 1)) n=1

A: The given series is: ∑n=1∞tan-1(2n+1)-tan-1(2n-1)

Q: 1 Find the general Solution of the following equa tion ; xy'-2y=x²

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: Question 3. Show that n3 + 4n2 +1 O(n²). %3D n+3

A: See the attachment

Q: Solve the initial value problem. where A = 1.5 -2 -8 2 -2 x' = Ax, x(0) =

A: Given : x'=Ax, x0=-21.5 where A=-2-82-2 To find : solution of the initial value problem.

Q: 38 4. Find L-1[e+7)]. '(2s+7 s2+16 5. Find L-') 6. Find C-1e (s–3)(s+1) 7. Find L-1 24e-5 82-9

A:

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Q: 9n – 5 a) lim n-- 3-n - 18 1 2n2 + 3n – 5 8n? +1 1 b) lim n- o0 || 4

A:

Q: 3) Solve the Initial Value Problem. 0 -1 X' = 2 0 X, X (0) = 5 |-1 2 4 5

A: Given the initial value problem

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Q: a(1 – rª ) n³(1-0.5'g(n) ; (1 – r) (1-0.5) (n³ – n³+0.5!g(n)) 0.5 =(2n3 – – 2n² ) 2 * n³ * 0.5'g(n))…

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Q: {in(n² +1) Im(x +4)} 19. А. В. 1 С. 1/2 D. 2 E. Divergent

A: we have to identify the given sequence is convergent or divergent

Q: (a) {cos ((2n + 1)E)-1 n=1 (Ъ) e2n+1 n=1 (c) n³ + n² – n2 + 3 - 1 | n=1 (d) {nsin 프}. n n=1

A: due to time limit I am able to solve first 4 part

Q: nx) in the E 2n is

A:

Q: 1. Expand x³y²(x + y)12. E15.(15) xn+3y15-n ,15-п а. n 12 b. Eo () xn+3y14–n ELo (5) xn+3y14-n С.…

A: From the given information. The given expression is .

Q: Find L {(2 t" – 3) (t +2)} O 2(2n)! n! + s2n+1 6 sn+1 2 (n²!) n! n² +1 sn+1 O 4 n! n! + s2n+1 8n+1 O…

A:

Q: Find L {(2 t" - 3) (t +2)} O 2(2n)! n! -- $2n+1 sn+1 O 2(2n)! s2n+1 n! sn+1 O 2(n²!) n²+1 n! sn+1 O…

A: To find:- L{(2tn-3) (tn+2) }

Q: n=1 B. E(-1)"- In n n=2 1 Inn c.(-1)"+1. n- Inn (-1)*+1. n + n=1 E.(-1)" sin(n) n=1 E(-1)"- n=2…

A: This is a problem of series calculation. based on the several available tests we can determine which…

Q: Find the radius of convergence and interval of convergence of  Σ 1 to infinity…

A: Given

Q: Solve the initial-value problem -2 x' = -1 х, 1 -2 x(0) 3

A: Given information: x' =-201-2x  and x0=-13 Calculate the initial value.

Q: Problem 5.3 Prove that n n(n + 1)(2n + 1) (3n² + 3n – 1) - Σ- 30 j=1

A: We have to prove given result by Principle of Mathematical Induction.

Q: 8. The solution of the initial-value problem x' = 5 )x, x(0) = х, is: (o) x =*" ()-*() 6) x = +()+**…

A:

Q: Solve the initial value problem dt 5Vi, y(1) = 9. (Use symbolic notation and fractions where…

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Q: Solve the given initial-value problem. I'= 2r, -1- 4x, + 2et x= 2x, - 4x, + 3et 1, =x-21, +et given…

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Q: 1 Homemade 5: Find exp ( t and use it to solve the initial value problem -9 -6 ): [8]-[] x(0) -- -6

A: The coefficient matrix is A=01-9-6,  and  X=xy. Find the eigenvalues and eigenvectors of A.

Q: Consider the initial-value problem y - 3ey = xe", with y(0) = 0. Find y(-1). . Note, y(-1) = In…

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Q: 2.5.3 Example C The equation Yk+1 – kyk = -e-1, ar = k and br = e-1, (2.97) has the particular…

A: We want to prove that yk=e-1∑n=0∞1k(k+1)⋯(k+n) is the solution of the difference equation…

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Q: Evaluate the given sums for number 5

A: Given,

Q: (k) E(-1)"-1. n+1 n=1 Vn +1- Vn – I (1) n=1

A: The given problem is to determine whether the series is converges or diverges using the appropriate…

Q: 7. E(-1)"- Vn +1 n=1

A:

Q: 1.4. E e-2k k=0 1.5. (-1)* k=0 k+1 1.6. k=53 k-1 M8

A: To analyse the given series.

Q: n +1 5n An bn n + 2' 4n2 – 3' { 400/n -1/(400n2) n even { Į 7 n/(1+n²) 1 901 п оdd Cn dn

A:

Q: 3RD ITERATION: x₂ = 3-X₂ +2₂ 3-1 + 1.1875 = 1.0625 3 3 Yo= 7-2x₂₁-22-7-2 10.757-1-1875 4 4 1.078125…

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Q: 1. Mr. Tejas has a total investment of Rs 10,000 in 3 bank accounts, one paying 5% interest. another…

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Q: 1 al 1z(z -4)e – 4)e z=1

A:

Q: How does h(n) = n2 /2n behave for large whole-number values of n? Does h(n) tend to infinity?

A: