n-1 For all n > 2, 4+ 3n4" – 4n+1 - j=1 9.

Q: La función f(x) =* expresada como serie de potencias es 4-х xn+1 А. 22n+1 n=0 4xn+1 В. 22n+1 n=0 C.…

A: Given function is fx=2x4−x. We have to find the power series representation of the given function…

Q: 7- y" + xy = 0, 20 = 0 > Answer Solution Let y = ao + ajx + azx²+.+an¤"+... Then y" =n(n – 1)a„x"-²…

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Q: solve xy' - y = xkyn, 1) y¹ – O a. (k+n O b. (k+n O c. (k+n O d. (k+n - - n 1) x¹ - n - 1) x¹ − n 1)…

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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: 3. Sum of coefficients of terms which contains integral powers of x in the expansion (2+ /x )30 is-…

A: We have to find sum of coefficient of terms which contains integral power of x:

Q: 1 ER=1 (- 100 k%3D1 2k+1

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Q: The series 2 ÷, n =0 x" |x| >1 has a sum equal to: Select one: а. х b. х— 1 C. 1 1-x d. 1 х —1

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Q: Journal: XFactor: n+4n- 12

A: the factors are (n-2) and (n+6)

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(z) = z(z+2) (z-1)(z-3) x(n) = u(n) — 223¹u(- -n-1) x(n) == Option 3 3 5 )=-u(n) + 3"u(n) Option 4…

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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: 4n+1 -a) Find the sum of this series Σn=071 3x 8-x²-y² b) Evaluate dzdydx

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

A: See the attachment

Q: 6) calculate In (2e°)= 11 2= 0.7n 3= 1. || ln5=1.6n7=20 %3D n(2e°)=X L ex =In 2

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Q: 8. A single cholera bacterium divides every 0.5 hour to produce two complete cholera bacteria. after…

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

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Q: Which of the following is TRUE? 2x2+1is n(x2) since Cx222x²+1 for all x 21 where C=3. OA. n is a (n3…

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Q: neN's ;i- n(n+1) 2 JKI Ŝ i - n(n+1) لكل

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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

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Q: 10. The sales of Universal Systems in the 1st t years are given by:S(t) = tv0.2t2 + 4 where S(t) is…

A: Sales of universal systems in the 1st years is S(t)=t0.2t2+4 we have to find the average yearly…

Q: Find Pr (|w| < 0.2)  where W ~ N (-1,4)

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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: 2 3 () is equal to 1+ (x – 1) 1) Show that the sum of the series 1+ 2 +.. +... (x – 1)2 + (x –- 1)³…

A: We have to solve given problem:

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 a recurrence formula of the n" coefficient of the power series solution to the differential…

A: First we have to assume general series solution for this given differential equation.

Q: 00 n + 1 is divergent. If we multiply any constant (labeled as h)to the n + 1 such that n + 2 n=1 n…

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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: x(х — 2)у" — бу %3D 0 about x =1

A: Given differential equation xx−2y''−6y=0 We have to find the power series solution of xx−2y''−6y=0…

Q: 4. Compute the exact value of (-1)"(n+2) xn+1 Ln=0 2n+1 (nt1) 100

A: The geometric series formula is ∑n=0∞rn=11-r, where r&lt;1. Break the numerator of the given…

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: 5.6) Apply the integral test to the series 1+e2n n=2

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

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Q: cos(n) /n Зп + 6 0 cos? (n) /n NA 1. CONV 2. n3 0 8n° – nº + 3/n 3. CONV 8n8 -n³ + 4 00 3n3 DIV 4.…

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Q: (i) Determine the number g, of ways of tossing a coin n times so that the combination HT never…

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Q: 4 Represent the function as a power series f(x) = (1 — 2г) n=0

A: We know that  (1-x)^n = 1+x + x² + x³ +........ Using this we can solve given problem

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

A:

Q: Find the recurrence relation for the power series solution about x=0of the differential equation y"…

A: Please see the answer in step 2.

Q: 2 - = 3t y+ x' = 3et * (0) = y (0) = 0 OL (x) = 3s2 (s+1)(s–2)(s²+1) 3(s-1) OL (z) = 76+1) (28²+1)…

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Q: 1 Integrate

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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) nt 2 xh l 1+2) 드 he (-1)" (n+ 2 2n+1(n +1 e exact value of )' n=0

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Q: Uses series to solve 2D^2 y + xy + y = 0

A: Please check the equation , there is no first order differential of y,

Q: Find the nth term of (a, b, a, b ... ), (a) and .(b) are constants 1-(-1)" 1- (−1)n+1 -[-D" + 2 2 a…

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Q: Graph the functions

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Q: -1)" (3n+2)| x2 By differentiating 1+x3 En=o[(-1)"(x)3n+2] , find the exact value of E-o 8n

A: Given: x21+x3=∑n=0∞(-1)n(x)3n+2To find: The exact value of ∑n=0∞(-1)n(3n+2)8n By using…

Q: 2. (50) Show that the differential equation 3x°y" +2xy' + a*y = has a regular singular point at x 0.…

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

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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: b) Find the recurrence relation for the power series solution about x = 0 of the differential…

A: (4) Consider the given expression: The general term for the series is,

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.