(-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)" In(n + 1) n=1 n=1

Q: 1 E * and g(x) = (- 1)" ", find the power series of (f(x)- g(x)). If f(x) = %3D 1-(-1)" | n 2.

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Q: 1 1 Express the series ) as n=1 (x – 9)²n -1 (æ – 2)²n – 1 a rational function.

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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: „7n – 4 Find the sum of the series: n! n=0

A: Given series,    ∑n=0∞x7n-4n!

Q: 8*+2 11k–1 k=1 The series diverges ||

A: Given problem:-       To find:- Given series divergent or convergent and find its sum

Q: (b) g(x) dæ 2+ x2 =

A:

Q: 1 is 1– 2x A power series representation for - Σ а. 22n for |a| n=0 b. Σ 2n for x< 1 n=0 C. 1 (2x)"…

A: We have to choose the correct answer

Q: 2n 28.What are the first three terms of the series n=1 O A. 2 4 6. x2 x4 O B. 2 4 6 X x2x O C. 2 4…

A: Explained below

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: (-1)"4"+1,n+1 3n+1(n + 1) In this problem, we investigate the power series n=0 Σ (-1)"4"+lpn+1…

A: We have to find the power series.

Q: > (-1)" x3n+2 find the exact value of 5-1)"(3n + 2) By differentiating the power series 8n n=0 n=0

A:

Q: "he reduction (recurrence) relation obtained for n 2 2 using the power series around the x = 2 point…

A: Note: n is dummy index here so we can replace n by m any time.

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…

A:

Q: (-1)"(2x + 4)" The power series n² 8" n=0

A: Given: ∑n=0∞-1n2x+4nn28n

Q: You are told that the recurrence relation for a differential power series question like we have been…

A:

Q: (-1)* Catalan's constant is defined by K = (2k + 1)2 * k=0 How many terms of the series are needed…

A:

Q: 2n x2n and S(x) 32n 2n + 1 If C(x) : r2n +1 32n +1 find the power series of C(x) + S(x). n=0 n=0 n=0

A: Given: C(x)=∑n=0∞2n32nx2n and S(x)=∑n=0∞2n+132n+1x2n+1To Find: C(x)+S(x)

Q: ny +y' = 0 by the power-series method. %3D

A: Let y=a0+a1x+a2x2+a3x3+…+anxn+… be the solution of the given differential equation. Now…

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: 1 1 Express the series > + – 1 as a rational function. n=1 (x – 6)2n- (æ – 3)²r 2n – 1 -

A:

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: cos(n") In(4) 1. 1 2. n In(n) n%3D 6n + 3 (-1)" n=1 1 4. n - 5 3.

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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: b) Even though x=0 1S an ordinary Point of a diff evential equation ,explain good idea to try to why…

A:

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: 2. Multi-Step Series E sin(n) n2 а. b. E sin(n) n=1 n² – 5 n=1 -

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Q3. Express into partial fractions. Hence obtain the sum of the first 3 What is the value of S ? k=1…

A: Partial fractions

Q: The power series 3(-1)" 2n+1 n=0 at x=-1 is equal to 1 3/2

A: We will find the value of the power series at x =-1 as following.

Q: (-3)"r" ice of the power series Vn +1 n=1

A: Series

Q: 19. What are the first three terms of the series =1 CO ? 2%3D1 2 4 6 A. А. - 4 6. - - С. 1. - x3 -…

A:

Q: (-1)*(x – 15)* Give the antiderivative, F, of the power series so that F(15) = 0. >, kk a) OF = E…

A:

Q: 5n – 1 Find the sum of the series: ) n! n=0

A: We have∑n=0∞x5n−1n!

Q: 5. Find the series solution of y" + xy' + y = 0. Show all the work. Be extra neat and clean and have…

A: Given DE y''+xy'+y=0 …………………(1) Here, P0(x)=1 , P1(x)=x , P2(x)=1 At point  x=0 : P0(0)=1≠0 So the…

Q: (-1)"(x+2)" The interval of convergence of the power series n=0 (n+1)422n A. -65x<2. B. -6<x<2. C.…

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Q: 2(2n) 3" (x+1)" n=00 Find the radius and interval of convergence for series Σ 12n n=1

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Q: (-1)"(2-5-8.(3n+2))(x-1)2n+2 3n. (n2 +1) The derivative of the power series f(x) = 2 %3D is n=0 f(x)…

A:

Q: 6. (a) Find the Taylor series for f(x) = e-2* centered at a = 3. For what x-values is f(x) equal to…

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Q: The power series 3(-1)* 27+1 n=0 at x=-1 is equal to O 3/2 O3

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Q: 00 1 Express the series 1 as a rational function. (a – 8)2n –1 (x – 5)²n-1 n=1

A: To express the series as a rational function

Q: (-1)"-2 (e) Alternating Series Test: 3" + 3n n=0

A:

Q: (2a) Give the Taylor series expression of - f (x) + g (x) Answer for (2a) | : т-1 E (-1)"- _< (m) –-…

A:

Q: Q.20) If ef(x) = 3x² +4, then f'(x) = a) 3x² b) e-f 3x²+4 3n 71 tements applies to the series En-1…

A:

Q: - 0.25k2 Find the smallest number n of terms needed to obtain an approximation of the series 27ke…

A:

Q: (-1)"4"+1µn+1 3n+1(n + 1) In this problem, we investigate the power series n=0 (-1)"4"+1pn+1 3n+1(n…

A: We have to find the power series.

Q: Evaluate E-2(1/(k² – 1)) by finding the limits as n→o of the series' nth partial sum.

A:

Q: What is the Maclaurin series of f(x) = 20 e ¯×?

A: We have to find the maclaurin series of f(x)

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: Find the Taylor series generated by f at x=a. 5. x)= 31

A: To find the Taylor series generated by the given function

Q: Q4/Using power series solve (y"-y=O)

A: The given second order differential equation is solved by assuming a series solution y(x) =…

Q: (-1)"x²n = E-0 x" and cos x = 0 100 For #6, given that find a power series 1-x (2n)! representation…

A: