Find the sum of each series in Exercises 45–52. 4 6. 45. У 46. 2 3)(4n + 1) (4n (2n – 1)(2n + 1) n=1 40n 2n + 1 47. E | (2n 48. n'(n + 1)² 1)°(2n + 1)2 =D1 n=1 1 50. E n=1 \2/n 49. E Vn Vn + 1. 21/(n+1), n=1 1 51. У In (n + 2) In (n + 1), n=1 52. E(tan-(n) – tan¬1(n + 1)) n=1

Q: Find the Power series solution , handwriting solution х^2у"+ху'+x^2у-0

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Q: The Taylor series of the function f(x) = e-* about xo = 1 is Select one: Ο Σ e-(-1)" (x-1)" n! (-1)"…

A: We have to find the Taylor series

Q: 15. Find the function represented by the power series Σ for all r<0. (2n)! (a) cosh(VE) (b) cosh(…

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Q: Section 7.1 Problem A Differentiate the power series representation of f(x) Section 7.1 Problem B =…

A: Please see the below picture for detailed solution.

Q: solve x^2y′′−4xy′+ 6y= 0 (not using power series)

A: solve x^2y′′−4xy′+ 6y= 0 (not using power series

Q: (n, 15) 1 and o(n) = 56, find o(75n).

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Q: 10. Find the Maclaurin series of (1+). (b) È(")(-)" (e) Č(")(-)" -2n (a) E(") (;)" 11. Find the…

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Q: As a general rule, is it advisable to difference a  time-series more than 1–2 times? Why or why not?

A: The objective is specify whether it is advisable to  difference a  time-series more than 1–2 times.

Q: Derive the power series solution around xo = 0 for the ODE 2x(х + 1)у" + 3 (х + 1)у' - у = 0…

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Q: [5] Determine the y(2021) of y=cos²

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Q: Evaluate the following telescoping series or state whether the series diverges. 1 1 Σ (n+1)* 102. 13…

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Q: Rewrite the series m=3 am x+1 -x Lm=1amx+3 as a single power series whose general term involves xm.…

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Q: Let X - Poisson(a). Show that E X(X - 1)(X- 2).… (X – k)] = ak+1

A: We are given that: X~Poissonαfx=e-ααxx!         x=0, 1, 2,....

Q: For any positive integer n, prove that summation d divides n t(d)^(3) = ( summation d divides n t(d)…

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Q: For z > 0, 옮(1 In (t³ + 1) dt A) In (x³ + 1) B) In (8z³ + 1) c) 2 In (z³ + 1) 2 In (z² + 1) D) 2 In…

A: Solution: Consider the given that; ddx∫02xlnt3+1dt We have Leibnitz Rule: ddx∫a(x)b(x)f(x,t)dt =…

Q: The power series representation for the function f(z) – is 9+ zª а. 2(-1)n2?n+1 E(-1)"* n=0 O b. 1…

A: One method is to use Tylor and Laurent series method which is quite complicated.  However, as the…

Q: 1 Ei=1 limn→00 n+i 2]

A:

Q: 3: You are given that the Fourier series expansion of f(x) = x2, x € (-7, 7) with period 27 is +4…

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Q: Show that the Fourier series of frx)= x² in El, 1] is x2 (-19^ 4 CosnTx, and hence show that n2 n=}…

A: Given function is fx=x2 in -1,1. We have to show that the Fourier series of fx=x2 in -1,1 is…

Q: Substitute x = 1, n = 9, and p = 0.18 into the binomial pmf formula below and solve. (Round your…

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Q: Solve x^2y′′−4xy′+ 8y= 0 (not using power series)

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Q: If the n th partial sum of an infinite series is Sn = 4n2 − 3/ 3n2 + 4 , what is the sum of the…

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Q: 11. Find the Maclaurin series of (1- a)-. (a) E(") ()" (1) È(")(-)" -2n (e) E(")(-)" 72 12. Find the…

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Q: Additional Problem A* (related to Section 5.5) Consider the series E(-1)n+1n/4" where the sum is…

A: The given series is ∑n=1∞(-1)n+1n4n. Alternate series error bound Theorem: If the alternate series…

Q: A/ Show that as a half range series of cosine terms for 0 < x < 1, π² /cos 2x cos 4x cos 6x +- +…

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Q: Use the identity 1 Ey" to express the function as a geometric series in the 1- y n=0 indicated term.…

A: The given expression is x1-x32 in x. Note: 11-y=∑n=0∞yn  if y&lt;1, Here, ∑n=0∞yn is a geometric…

Q: Find J 15x(4)* - dx

A:

Q: اذا كان )) In =2 متسلسلة فان متتابعة المجاميع الجزئية )) S = #=1 ln هي M M b)ln (M) c)ln M e)ln(M –…

A: Given  SM=∑n=1Mlnn+1n

Q: Let 2 (-1)** 'ak be a convergent alternating series with terms that are nonincreasing in magnitude.…

A: We have to find the upper bound for  error.

Q: A/ Show that as a half range series of cosine terms for 0 < x < 1, π² /cos 2x cos 4x cos 6x +- 6 +…

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Q: The power series 1+2 (x+9) +3 (z + 9)² +4 (x + 9)"+ is centered at O z= 9 O I= 0 O I=1 O I= -9

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Q: •()(2x² + 2x) (4)" ()" 40-x The sum Lx=0 0=x" 230 335 435 None

A: The given equation is as follows: ∑x=040Cx402x2+2x14x3440-x Need find the summation value of the…

Q: EXAMPLE 4 Only One Series Solution Solve xy" + y = 0.

A: NOTE:- By Bartleby rules, only first question is solved Given equation is xy''+y=0…

Q: .Find a sequence that diverges, but doesn't diverge to infieity (a) an = n+1 (b) bn %3D Vn +1 (c) Cn…

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Q: 1/(1-2) + 1/(2-3) + 1/(3 · 4)+.....+ 1/{n(n + 1)} (a) n(n+1) (b) n/(n+1) (c) 2n/(n + 1) (d) 3n/(n+1)

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Q: 27 Find (all) the value(s) of c such that 3c2n 8. %3D n=0 (A) c=3 (B) с 3 4 (C) c=-33 (D) c = } (E)…

A: Substitute the value of c as 0, 1 and 2 in the nth term to find the generated series.