2 an IS AB5OLU TELY CONVE RGENT! unbuznuo7 si juniz Convergent 7 E E\anl is divcrgent but Ean is convergent a E An is CONDITIONALLY CONVEKGENT!

Q: E Suppose we also know that 1 > an > 0. and a converge. Then the series > converge 1-an Select one:…

A:

Q: 1 is not convergent. Theorem 1.8.2 E n = 1

A:

Q: converges, because 0 < 1 and an %3D debook 2n + 1 2n +1 2n +1 Room

A: We have to choose the true or false

Q: De termine whe er me sones conve rges aosolude ly ,converges conditionally ,o di verges زاس

A:

Q: 5. Let ni < n2 < n3... be positive integers, and let E = x E [0, 27]; sup converges. Show that E has…

A: Given :  n1≤n2≤n3 ...  be the positive integers and E be the set defined as ;                E =…

Q: find the value of p which the inegrad converges absauaysconditionally COSY

A:

Q: Consider an = V4n2 + 3n – 2n for n 2 1. - (a) Determine if {an}, n=1 is convergent or divergent (b)…

A: Here, an=4n2+3n-2n, n≥1     =4n2+3n-2n4n2+3n+2n4n2+3n+2n     =4n2+3n-4n24n2+3n+2n     =3n4n2+3n+2n

Q: 3.3 Prove that does not converge uniformly on R. k! k=0

A:

Q: What is the largest positive constant K such that if 0 <r < K, then (nl)2 must (2n)! n=1 converge?

A:

Q: If C.)" converges, then C,)" converges. n=0 n=0 Select one: True False

A:

Q: Ee whether or not fn converges uniformly nclusion. b) (0, 1)

A:

Q: Show that E-2 ((In n)ª/n²) converges for -o 1. n=2

A:

Q: Suppose that X₁, X2, ka)=P(X = _k) =1/2. Let Yn = Xn = n 2 Xi. are independent, such that, for each…

A: Chebyshev's Inequality Chebyshev's inequality guarantees that for a large class of probability…

Q: determine whetheer the fene Conditionally (Convergent,abtolutely onvergent or dirergent a . n= 5…

A: We have to find whether the sequence is convergent or divergent and to know whether it is absolutely…

Q: 1. Prove or give counterexample. (a) If (xn) and (Yn) diverge, then (an + Yn) diverges. (b) If (xn)…

A: According to our guideline, we can solve first three subpart of a multipart question. If you want…

Q: If o an is convergente then o nan is divergente Select one: O True O False

A:

Q: the valu e of P. for ubich for allna). fntegral Converges

A:

Q: 4. Does cosnx uniformly converge in [a,b] c (0, 7)? n =1 n

A:

Q: (c) Show that fn (x) : x2+n? converges uniformly on [0, 0).

A:

Q: If 2, =1ª, converges conditionally then E=|92| diverges 'n=D: Select one: True False

A:

Q: Corver Is absdutely contergent, Conditionally Convergent, on divergent

A: Use Alternating series test, P- series test

Q: n=1n2 +1 converges using 2 n =1 diverges using n =1 converges using 2 n =1 diverges using n =1 else…

A: Infinite series is the sum of the infinite sequence. A series is convergent if the sequence of…

Q: H.w. which of the fellewing serier absolutely converge and which eonditionally convere.

A:

Q: (b) Prove that the improper integral ]] 8888 converges. dr dy (1 + x² + y2)3/2

A: Solution: Given improper integral, ∫-∞∞∫-∞∞dxdy1+x2+y232 As we know the convergence of the series is…

Q: #2. Give a counter exa mple that (Sn) is bounded but not convergent.

A:

Q: Q3: Show that 3(2)n+2 3(2)n+2 is convergence and En=0 5n Zn=0 5n 20.

A: Please refer to the image below.

Q: 13. Determine whether ∞ Σ(-1)* k1/2 k=1 converges absolutely, converges conditionally, or diverges.

A: The given series,    ∑k=1∞-1kk12

Q: 16) If E an converges, then cos(am) diverges. n=1 n=1 a) True b) False

A: According to Bartleby's policy we are allowed to solve only 1 question at a time. Here's the…

Q: (2) If £ an and D bn are both divergent then is E an · bn necessarily divergent? If yes, provide a…

A:

Q: 3 If Xn 4 and ly,l0. Select one: True O False

A: Given, xn → 4  and  yn≤31n2n for all values of n To determine whether ∑ xnynp  is absolutely…

Q: 2. Prove that (1,1,1,...) converge to 1 in (R,).

A: Convergence of the sequence

Q: If E an converges, then an/n12 converges. n=1 n=1 O True False

A: True, using Abel's test.

Q: (c) Prove that if there exists an M &gt;0 such that |fn| ≤ M and |gn| ≤ M for all n ∈ N, then (fngn)…

A:

Q: Hiw.which ef thefellowing serier which conditiunally converge absolutely converge and

A: Find the sum of the series.

Q: Let 1 = S dx c+∞ 4-x I = dx Then I O converges to 3 O converges to .

A: Consider the integral: I=∫1+∞4-xx3dx

Q: I En=1 an converges then 2a, converges.

A:

Q: Dis cuss the Conditions For which Foun'er sevies is conv convergent ·

A: The objective is to show the conditions.

Q: 2.62 Show that fn(x) = x+n converges uniformly on [0,1] but not on (0, 0).

A:

Q: Consider the sequence S n²r(1 – nx) x € [0, 1/n] - fn(x) := 0. elsewhere . Show it converges…

A: Let gx=n2x1-nx Differentiating wrt x, we get  g'x=n2-2n3x Putting g'x=0, we get  n2-2n3x=0⇒x=12n

Q: Lütfen birini seçin: a.Converges absolutely b.None of them c.Converges conditionally d.eventually…

A:

Q: The sequence {C+1 In=2)"} N=1 converges to e² O None diverges converges to le converges to e³

A: The given sequence 3n+23n+1nn=1∞ The sequence can be written as follows:…

Q: 1 If ° 굶 dr 3D품. Then Σm1 00 +1 Select one: O a. converges to . b. converges but is not the sum of…

A: Answer and explanation is given below...

Q: The set S on wc fn Cx) = 1+ x" Converges pointwire ?

A:

Q: Does E 8. k=1 In(ek41) converge or diverge?

A:

Q: (iv) We say {fn} converges uniformly to f(x) iff (Ve > 0)(3n > 0)(Væ)(n >n=\fn(x) – f(z)| < c). What…

A: (Part 4 ) only asked and answered

Q: (b) Use the Weierstrass M-test to show that E(cos.x)". 4 n=0 converges uniformly on [A/4, 37/4].

A: The series is given by: ∑n=0∞cos x2n,    x∈π4,3π4 Now, ∑a2n=a0+a2+a4+... Now, cos function lies…

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

A: