100 4. If En=1 an converges absolutely, then n=1 an converges conditionally (C). 1 For p > 1, the root test applied to Ln=1 n is inconclusive (C). 5.

Q: Do the following sequences {a} converge or diverge? Justify your answers (a) an 3" (b) an - (-1)"/ñ…

A: Explanation of the answer is as follows

Q: 6. The probability of convergence of a sequence of independent random vari- ables is equal to 0 or…

A: The probability of convergence of a sequence of independent random vari- ables is equal to 0 or 1.…

Q: Which of the followings are true? 1.En=1 7?+Inn (-1)" is absolutely convergent. II. >n=1 (-1)m is…

A:

Q: Both of the following series converge by comparison to En=12 3 3 and 24n² + 7 24n2 – 7 n=1 n=1…

A:

Q: Which of the followings are false? I. 0 (-1)" is absolutely convergent. Ln=1 n² +Inn 2n II. E (-1)…

A: we have to check each options

Q: p for which In (n) Comvenges

A: Given∑n=1∞ln(n)np

Q: n3 Use the limit comparison test with the p-series to determine whether S 2n5 – 4n – 1 converges or…

A:

Q: determine if weather the given series of functions converges {Sn(x)} = {_ a*-'} uniformly or not k=1…

A:

Q: 2 3 - ( ² ) + ( 3 ) ² + ( )*²+ + converges to until you find an SN that approximates with an error…

A: Solution :-

Q: et r ER. Find all r for which [(n≥2) 1/ (n (logn)^r)) converges.

A: Series is a combination of the term of the sequence. The convergent series is defined as convergent…

Q: D) { (-)"} [Select] [Select] converges to 2.

A: Please see the below picture for detailed solution.

Q: 26. The series converges when 2n A. r>1 B. r<1 C. r = 1 D. r = 0

A:

Q: 3. Let F(x) = sindt. cx (a) Show that F(x) = x- 3.3! x5 + by integrating an appropriate power…

A:

Q: What is the value of p = lim+¹ when applying the Ratio Test to assess n→∞an a convergence of? What…

A: Given problem:-

Q: 21. Show that E(-1)"+1; 2n converges n! absolutely. n=1

A:

Q: 6. Find the interval of convergence of -x* . Where p >0 is a fixed constant.

A:

Q: Show that the p-series ∞∑n=1/1np converges for p&gt;1.

A: We have to show that the p-series ∑n=1∞1np converges for p&gt;1.

Q: 17.Show directly, using the ratio test, that the two series solutions of Airy's equation about x = 0…

A:

Q: 3. Let F(x) = sindt. (a) Show that F(x) = x −· 3.3! 5.5! 7.7! + by integrating an appropriate power…

A: The objective of this question is to express the function F(x) = sin(x) as a power series and then…

Q: Suppose that dz converges. What can we conclude about the constant p? Op>1 Op Op< 3

A: Explanation of the answer is as follows

Q: Let f(x)= cos x and derive its Maclaurin Series, and find its interval of convergence.

A: We have to derive the Maclaurin series and interval of convergence for f(x) = cosx.

Q: 3. Suppose that the power series c(-2)" converges for r-6 and diverges for r=-6. What must be true…

A: It is given that the power series ∑n=0∞cnx-2n converges when x = 6 and diverges when x=-6.

Q: Find all values of x for which each power series converges. Σ •a. (x +2)" l=ח

A:

Q: - Convergence in mean square, If a sequence of r.v. X₁, converges to X in mean square, with E[X²]…

A: Given information: The information about convergence in mean square is given.

Q: If an < bn and if En=1 an converges, then 1 bn also converges. True False

A: we can solve it by using comparison test.

Q: 8. Use the limit comparison test (Section 11.4) to show that the series Σ tan 3n n=1 is convergent.…

A:

Q: Assuming a series of 5000 values of Y, with Var(Y,) = 81. Suppose that p=(-0.2)K| . Then Var() is…

A: Assuming a series of 5000 values of Y, with Var(Y,) = 81. Given that Px=(-0.2)|k|

Q: 1 n(ln n)5 n=2 is convergent. (A). According to the Remainder Estimate for the Integral Test, the…

A: Given series ∑n=2∞1nlnn5 (A) S−Sn≤∫n∞1xlnx5dx Substitute  lnx=u ⇒1xdx=du And limit of u is lnn to ∞…

Q: Which of the followings are false? is absolutely convergent. 1. Ln=1 (-1)*-1 is absolutely…

A: