Match each of the following with the correct statement. A. The series is absolutely convergent. C. The series converges, but is not absolutely convergent. D. The series diverges. (-1)n 5n+5 2. (-6)" 3. < 5. n=] 00 n=1 ∞ n=1 n=1 n2 (−1)". √n n+10 sin(5n) n2 (n + 1)(6² − 1)n 62n

Q: (-1)*+1 1 = 4 ) 2n – 1 n=1 = 4 -+- + - 8.

A:

Q: Which of the followings are convergent series? 5+2" n=1 2+2 00 1. 1 II. En 1 4n -1 00 . Σ (sin1)" .…

A:

Q: a 'n+1 If the power series 2a (x- d)" is such that lim n=1 a L 00 - Which one of the statements…

A:

Q: M8 M8 Με 4. Σ 15. Σ 6. Σ n=1 (n + 3)" 47² nt 1 – 5η4 (n + 3)" 4" η

A:

Q: Match each of the following with the correct statement. A. The series is absolutely convergent. C.…

A:

Q: A. The series is absolutely convergent. C. The series converges, but is not absolutely convergent.…

A: "Since you posted multiple questions, we will provide the solution only to the first 3 subparts of…

Q: V. Consider the power series +∞o Σ n=1 (x + 1)n 3√√n² + 1 1. Determine whether the resulting series…

A: Use Leibnitz test(given in next page) to show convergence at x=-4.For 2) use radius of convergence…

Q: 2y dr - y dy y (x-2y) dy, y(0) =-1 O x = 2y - e +3 %3D a y = 2r- e+3 0x= 2y-e+3 O x = 3y + 2e +1

A: Given DE is 2y dx-y dy=y(x-2y)dy ⇒dx-12dy=12(x-2y)dy⇒dx=121+x-2ydy⇒dxdy=12+x2-y⇒dxdy+x-12=12-y Which…

Q: Find the function represented by the power series. X+ 10 3 n= 1

A:

Q: Which of the following series is converges or diverges. If the series converges, find its sum? 2n+2…

A:

Q: II. Find the value(s) of x (or the interval of convergence) 2. Σn=0 for each of the following power…

A: The power series is  ∑n=0∞ (-1)n+1(x-5)nn·5n

Q: Consider the two series: 00 2n + 3 (a) n2 In n 00 1+ (n – 1)! (b) > n! n=1 Which of the following…

A:

Q: n x + 2 .? х — 1 5. What is the domain of convergence of infinite series 3n n=1 What is the value of…

A: we have to find the domain of convergence of the given series and also find the value of it at X=-1

Q: Using the limit comparison test, which of the following would prove the end behavior of the series?…

A:

Q: Select all the series that are absolutely convergent.

A: We have to find out the absolutely convergent series.

Q: A. The series is absolutely convergent. C. The series converges, but is not absolutely convergent.…

A: From the given series we have to check the convergent and divergent of the series.

Q: Which of the following is true? O A p-series is divergent if p > 1. none The series E(-1)" -1, 2 is…

A:

Q: Σ 22η n=1

A: