1 -dx x²+2x+5 -00 3n converges to O diverges converges to 3 4 O None converges to 4 converges to

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

A:

Q: Determine whether the series 5 + 2 sin(3n) 9" + vn n=1 converges or diverges. 8.

A: See the attachment

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: I. Consider an = V4n² + 3n – 2n for n >1. 1. Determine if {an}-1 is convergent or divergent. 2. Is >…

A: Simplify the expression of an. Multiply and divide the given expression of an by 4n2+3n+2n to…

Q: The power series > (2 – x)' converges absolutely on the interval r=1 (1, 3) [1, 3] (-2, 2)

A:

Q: The series Σ 6( − 1)*0.2-1.9/k○ diverges converges. k=0

A: We use ratio test to find the desired result.

Q: TL The series =o 2n +5 Converges to 1/2 Converges to -1/2 Converges to 4 Diverges Converges to 1/4

A:

Q: 9. -l x(x+5) dx converges, so the series converges. x3D

A:

Q: Which of the followings are false? 1 1. En-1 sin-| converges by comparing with 2 II. En-1 converges…

A:

Q: How to determine nln(n)/(n+1)^3 is convergent or divergent?

A: To determine the sum of the series nln(n)/(n+1)^3 is convergent or divergent. Now, Apply the…

Q: 2. Ln=0 (n+1)* If the series converges, use the Integral Test can be used to show convergence

A:

Q: ( n²x, 0<x<1/n fm (x)={ --n²x+2n, 1/n<x<2/n L 0, 2/n<x<1 uniformly convergent on [0, 1]?

A:

Q: +o0 (-1)*n" sin" () Σ 2n n=1

A:

Q: Q10) The series 4n Σ n =1 n²+2 a) converges to b) converges by comparison test th term test c)…

A: To find- The series ∑n=1∞4nn2 + 2  Converges to 0 Converges by Comparison test Converges by nth…

Q: dx Study the convergence of 1= Solution

A:

Q: cot(8)de is a) converges to - 1 b) converges to - 2 c) converges to -n d) diverges e) None of all

A:

Q: The sequence {()} Sn+3 Sn+1 n-1 converges to e converges fo te ConvCrges fe Ve Converges 00 Diverges

A:

Q: The series 2=1 1 k is divergent no conclusion absolutely convergent conditionally convergent

A:

Q: The infinite series Ln=1In(n+1 In(n+2) Select one: a. Converges to 0 b. Converges to In 2 c.…

A:

Q: The series Lk = 1 (-1)*+1 is 2k divergent absolutely convergent conditionally convergent none

A: First I have written a short note about Absolutely and Conditionally convergent series and find tha…

Q: Q.5. Solve by using L-Hospital rule, In x lim x-1 x- Vx Q.6. Determine whether the series Converges…

A:

Q: 0. The improper integral | x²+4x+8 -0- converges to 4 converges to 8. None converges to 4 diverges

A:

Q: 2 n 1 o Show that + converges/diverges n-

A:

Q: N 2N + 1 2) Show that converges/diverges. +

A: We have to show whether the series converges or diverges.

Q: 5n – cos 2n 3. Use Comparison Test to determine whether the series converges or diverges. n³ + n² +…

A:

Q: 3. The numerical series log O converges to a ptive number O diverges to+0. Odiverges to-0. O…

A: We can find whether the given numerical series converges or diverges using limit comparison test.

Q: ∑∞ ((−1)^n−1(1−n)) /(3n−n^2) n=1 Find if the series converges or diverges! Find the limit if it…

A: Topic- Series

Q: Vn + 5 Σ 3n2 + n + 1 n = 1 O converges O diverges

A:

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

A:

Q: Find two linearly independent power series solutions centered at x0=0 to y''+x2y = 0 state the…

A: Given differential equation is y''+x2y = 0.

Q: 1 x converges 1 ex - e-X Select one: True False

A:

Q: If a power series ∞ n=0 anxn converges absolutely at a pointx0, then it converges uniformly on the…

A:

Q: If the power series anx" converges only in the interval (-4, 4), then the series n=0 nan converges…

A:

Q: (-1)**l а, Ans. Converges, 0 7) 2n –1 2n 8) an Ans. Converges, v2 n+1

A:

Q: îf хи 1+nn } Convergent uniformy in [0,00) ?

A: Introduction: As a sequence of real numbers, a sequence of functions is also convergent or…

Q: n²x, 0<x<1/n fm (x)== { --n²x+2n, 1/n<x<2/n ( 0, 2 n<x<I uniformly convergent on [0, 1}?

A:

Q: The series 2n +2 Diverges to-o0 Converges to 1- Converges to B Diverges to +

A: Given series is ∑n=1∞sinπ2n-sinπ2n+2 The Nth partial sum of given series is…

Q: 1dx x²+2x+5 -00 O diverges O None 37 converges to 4 converges to converges to converges to 3r

A:

Q: Use comparison test to show that the series E=1 (2) converges. 5n2-п.

A:

Q: 8. 1 The improper integral xp: V(x – 4)³ 4 Converges to -1 Converges to -4 Converges to 1 Diverges

A: To find the improper Integral  Take (x-4) = t And the limits accordingly Then integrate and put the…

Q: 24) Identifa tue internel of convergen ce of a power ser's Ž (3)" n-1 (-3)", n=) a ) b) c) d) 3 2x23…

A:

Q: N + 1 2N 2) Show that converges/diverges. N-1

A: The given series is: ∑N=1∞N+12N+1 Let. aN=N+12N+1,N≥1

Q: 23. Suppose N is a positive integer, a, -f(n), and f(x) dx diverges. What does the integral test…

A:

Q: The sequence of functions fn : x → x" sin(x" +2) + x 1. converges pointwisely to x over (0, 1/4] but…

A:

Q: Can we use two ways to show 1 Σ n² +5n+6 n = 0 to n = infinity, convergent or divergent ? Say, 1)…

A:

Q: nºx, 0<x<1/n fm (x)= { --n²x+2n, 1/n<x<2/n L 0, 2/n<x<1 uniformly convergent on [0, 1]?

A:

Q: 1.4 Does (fa(r)} in 1.3 converges uniformly on |-3,3]? Explain.

A: