. Find the power series representation of f(x) = 3 using the geometric series 3+x 1 f(x) = 1 - ", for |a| <1 n=0 Give the interval of convergence of the new series.

Q: Q1. Test the following series for being convergent or divergent: 1 a.) E ne1 (In n)" 2 b.) Σ 1- 3n 2…

A: According to our company's guidelines I can only answer first question since you have asked multiple…

Q: 2. I) Find the centre, radius, and interval of convergence for the given power series. 1 Σ (13) n…

A:

Q: Σ -(2.r – 1)3". 14+1

A:

Q: 6. Are the following series convergent? Why? (a). (b) 00 n=1 α 2 (3n-1)1.3 n=1 n2 – 1 2η2 + η

A: The given series are ,  (a).        ∑n=1∞2(3n-1)1.3 (b).         ∑n=1∞ n2-12n2+n (.)  Necessary…

Q: The set of convergence of the power series Σ (x +5) n2(1+3") is O (A)[-8, -2] O (B) (-16/3,-14/3) O…

A: To find the convergence, we will use ratio test. D' Alembert's Ratio test: Consider the series ∑nan…

Q: 6. Find the power series and determine the interval of convergence of 3x f(x): x2+x-2

A:

Q: 3. Find the interval of convergence of the series ☎ n=1 (-1)"+¹(x-2)" 3"-n

A: Find the interval of convergence of the series

Q: Find the radius and interval of convergence for the following series: (x - 2)" 10n a. 8 n=0 Radius =…

A:

Q: 18. Find a power series representation for the function and determine its interval of convergence a)…

A:

Q: Find the radius and interval of convergence of the power series 3" (n!)212 (2n)! n=1 z"

A: The answer provided below has been developed in a clear step by step manner.

Q: F(x) = (-1)". n3n n=1

A: Given series ∑n=1∞(-1)nxnn3n

Q: Consider the series (-1)" (6x+5)" n=0 (a) Find the series' radius and interval of convergence. (b)…

A: We have to find- series radius and interval of convergence, values of x for which series converge…

Q: Find the radius and interval of convergence for the following series: (x - 2)" 10" a. 8 n=0 Radius=…

A:

Q: 5. Expand the function into a power series (a) Show that X 1- x - x² Σ n=1 fnxn f₁ = f2 = 1, fn+2 =…

A: In this given question We know that  1) If power series converges for |x-a|&lt;R Then Radius of…

Q: (5) Find the interval of convergence of the power series (n!)? a". Show your work. (2n)! n=0 IM:

A:

Q: For the power series Σn=1 (–3)” n find its interval of convergence. √n

A: The given problem is to find the interval of convergence for the given power series. Given power…

Q: E(-1)* sin () i=1

A: Given : ∑i=1∞ -1isinπn

Q: Find the radius of convergence and interval of convergence of the power series (-1)" (n + 1)4"…

A: The given power series is ∑n=1∞-1nn+14nx+2n. Here an=-1nn+14nx+2n, then an+1=-1n+1n+24n+1x+2n+1. Use…

Q: 8 (a) [-R, R) (b) (R-a, R+ a) (c) (a - R/2, a + R/2) (d) (a - R, a +R] (e) None of the above. n=0…

A:

Q: discuss convergence of series of functions of ∑ x/n(n+1) in]0,∞

A:

Q: 2. If the power series defined by En=1 an (x + 1)" converges at x=3, thenE-1(-1)" an…

A:

Q: 1. (Power series expansions) (a) Determine the radius of convergence of the series E 4n2" when:…

A: