Let S = (1 + (nx)²)-¹. a. Show that the series S converge on R\ {0}, but does not uniformly converge on this set. b. Show that if a > 0, the series uniformly converges on R\(-a, a).

Q: l x such that the

A: Here we have,  A=∑n=0∞(-3)nxnn+1=∑n=0∞an ⇒an=(-3)nxnn+1

Q: 3. Show that the series In 2+ (-1)k-1 -(x – 2)* k2k k=1 from Example 3 diverges when x = 0 and…

A: The given series is ∑an = ln 2 + ∑k=1∞(-1)k-1k. 2kx-2k.Putting x = 0, the series reduces to ∑an = ln…

Q: G₂- Let Sn = a; be the nth partial sum of the series . Suppose that S, is given by S₂ = 5- i-1 (a)…

A:

Q: Suppose that the nth partial sum of a series (∑∞n=1 an) is sn = (n-1) /( n+1). Is the series…

A: A series is aid to be convergent iff its partial sum converges.Find the limit of partial sum.

Q: Decide whether the given series are absolutely convergent , conditionally convergent or divergent.…

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: Find the largest interval (in x) where the series summation from n = 1 to infinite of xe-nx…

A: Here we use D'Almbert ratio test.

Q: 2 e -n=1 in"(e" +1)

A: Given query is to find the series converging or diverging.

Q: The series E is (i) Diverge (ii) Converge

A: The given series is: ∑n=1∞1n45 Which is of the form ∑n=1∞1np And p-series converges if p>1 and…

Q: 2 Σ e -n=1 In +1)

A:

Q: 4. Show that the series " is Convergent, but the (-1) squence s not summable.

A:

Q: Let Xn be a Poisson(n) r.v. for n = 1, 2, . . .. Prove that Xn/n −→ 1 (converge in probability)

A:

Q: 9.. For the series 1+n² a. Show that the series passes the divergence test (nth term test). b. Apply…

A: The given series is ∑n=1∞n1+n2. (a) To Show: this series passes the divergence test. (b) To Show:…

Q: For what values of x does the series, (-1)"(3 – x)" n4n n=1 a) absolutely, b) conditionally?

A:

Q: Σ n² – 3n + 2 n=3

A: Explanation of the answer is as follows

Q: 3) Consider the series of functions n Σ(12) (2)", ,XER. n=0 Prove that the series converges for all…

A:

Q: 4. Consider a power series of the form E anx". Suppose that lim sup Jan|/n = 0. Prove that the…

A: To apply root test, we transform given series to new series where x is taken arbitrary.

Q: 1.Does it follow that if an > 0 for all ne N, thenEn=1 an does not converge conditionally? Explain.…

A: We have to explain the given statement.

Q: 3. The value(s) of b for which the series E=50 is convergent are: 4 n3b2 B)는 C)- D)- (수-w-) n (") (M…

A:

Q: Determine whether the series 2-√√n +∞o Σ √√n n=1 converges or diverges using the Integral Test.

A:

Q: Using the extended CIF compute: (Justify your steps! iv) { 2 (1-2jadz - C is a simple, closed,…

A: