6) Show that the series L07-1 converges uniformly on n%3D0 (22-1)" (z: Iz| 2 2).

Q: 5k 3 k=1 k4+1 k%3D1 co

A: Follow the steps.

Q: Determine whether or not the series of functions {Sn(x)} = {> xk-1} converges uniformly on [-a, a]…

A: We shall use the basic knowledge of power series and notions of converges and we shall use the…

Q: 2. Find the interval of convergence of the series (n + 2)(x + 3)²n+2 2n

A: Here an=n+2x+32n+22n. The series converges if limn→∞an+1an<1

Q: Determine whether the series converges. V5k - 1 k=1

A:

Q: Since lim k→+0 (k + 1)!/3k+1 k!/3* k+1 lim k→+∞ 3 +00, k! the series…

A:

Q: 4n+3 Examine the convergence of the series En=o,AT by applying limit comparison test.

A:

Q: Find the interval of convergence of the series. (x - 4)n Σ 8+ 5n n=0 45 19 <x< 8 -1 < x< 9 -1 sxs9…

A:

Q: Suppose that a power series f(x) = L a„x" n=0 has the radius of convergence p > 0 and that L.- anp"…

A:

Q: Find the smallest value of x for which the series 00 (z+ 125)" is conditionally convergent. Yanıt:

A: We need to find the least value of x so that the series ∑n=2∞x+125n2lnn is conditionally convergent.…

Q: Vn 00 #1. E- n = 1 Vn° + 4n+3

A: As per our gudeline we supposed to answer only first question kindly repost other as next question…

Q: 2. Find the region of convergence of the series (3r)" +2

A:

Q: (-1)"xn Гоо Zn=1 Vn

A:

Q: 2. Show that the series is conditionally convergent. n=2 cos(nx) √n ln n

A: Solution of the problem as follows

Q: 2. Find the interval of convergence for the series. n=1 (x - 7) n n5n

A:

Q: 3. Give an example of divergent series n=1dn and Ln=1 6n for which the series ("q + "p) converges.

A: Given: that An example of divergent series ∑n=1∞ an and ∑n=1∞ bn for which the series  ∑n=1∞ an+bn…

Q: b) The series sin(n°r) and 1+n³ n=1 n=1 are uniformly convergent on (0, 1).

A:

Q: Suppose that the power series Сn (2а — 3)" n=0 converges when x = 5.5 but not when x = -5.5. If its…

A: see below the answer

Q: Show that the series -1 (2n+1)" converges absolutely. in=1

A: We will check its convergence by ratio test .

Q: 4) Find the interval of convergence for the power series F(-1)"-'n 2" t. n=1

A: Given series is ∑n = 1∞(-1)n-1n2nxn

Q: (x+1)* (+x) 3k k=0

A: Find the radius of convergence

Q: Find the radius of converges and the interval of convergence for the given power series. (х + 1)" 6º…

A:

Q: Does the series from 1 to infinity of ((-1)^(k+1)/((k+1)!) converge absolutely or converge…

A:

Q: Find the region of convergence of the power series (2 – a)" - 6"n n=1

A:

Q: 9. Estimate the value of the convergent series 8 k=1 (-1)^² k! + 2k with an absolute error less than…

A:

Q: Does the series from 1 to infinity of ((-1)^k)/(k^(2/3)) converge absolutely or converge…

A:

Q: 3. Find the open disk of convergence for the series (-1)"(x + 1)" Σ 2n n=0

A:

Q: The series k=1 5( − 1)k+1 - kl.1 O converges diverges.

A:

Q: Find the series' interval of convergence of (x* + * + })" x In(n) n2 n=3

A: Given series is ∑n=3∞x2+x+14nlnnn2.

Q: Since (k + 1)!/3k+1 lim k +1 lim k→+∞ 3 +00, %3D k→+0 k!/3k k! the series…

A:

Q: Consider the series 1 E(-1)"+1, (2n - 1)! n=1 (a) Show that the series converges using two different…

A: Given series is ∑n=1∞(-1)n+11(2n-1)! Let  un=1(2n-1)! then un+1=1(2n+1)!…

Q: Find the radius of convergence of the series. 2: 4 2k yk • 6 (2k)! k = 1 R =

A:

Q: Determine a minimum radius of convergence of a power series solution about x 2 to (x2 + x)y" + 3y' –…

A: We can solve as follows

Q: Find the interval of convergence of the series. (x - 5)" 4 + 9n n=0

A: Given,        ∑n=0∞x-5n4+9n

Q: a lower bound for the radius of convergence of series solutions for (x² - 4x + 5)y" + (x + 3)y' +…

A: Solution:Given the diffrential equationx2-4x+5yιι+ x+3yι +4x2-4x+5y=0The coefficient of yιι is…

Q: 2. Show that the radius of convergence of a standard binomial series (1 + x)a = Eo () (x)k is equal…

A:

Q: Find the series' interval of convergence of (x² + x + })" In(n) n2 n=3

A: The given series is ∑n=3∞x2+x+14nlnnn2 We have to find the interval of convergence. Let…

Q: Prove that the series of functions (2+1)(3+1) +,N0 is convergent on [0, 00) but the convergence is…

A:

Q: Find the nth Partial Sum S, of the series and also discuss convergence/divergence of the series. 1…

A:

Q: the root test fails to determine if the series Σ (1 + n= 1 converges or diverges

A:

Q: Find the series' interval of convergence of (x² + x +) In(n) n2 n=3

A: Consider the provided series, ∑n=3∞ x2+x+14nlnnn2 We need to find the interval of convergence.

Q: 1 – 4x)k Ek=1 k k3

A: In the question we have to find interval of convergence.

Q: Does the series from 1 to infinity of (k!)^2/(2k)! converge or diverge using the ratio test?

A:

Q: Does the series from 0 to infinity of (-1)^k/(2k+1) converge or diverge?

A:

Q: 5. Prove that the series converges using the corresponding test: n=1 (-1)+¹(X+Y+ 1) n²

A:

Q: Does the series from 1 to infinity of ((k!)^2/(2k)!)^k converge or diverge using the root test?

A: ROOT TEST

Q: +o0 2(-1)"+1 (x – 1)" n=1

A:

Q: 6) Show that the series Eo converges uniformly on (z:J2| 2 2).

A: Consider the given equation,

Q: Find the interval of convergence of the series (-2)*¹*¹ (x − 1)* 4* (k+1) k=1

A:

Q: 2. Find the region of convergence of the series (3r)" n +2

A: