If the lim,- (1+ = = e, then the series a, is Converge

Q: What is the largest value of x for which the series (x - 8)" n 4 is absolutely convergent? Answer:

A: FOLLOW NEXT STEP

Q: In  the given question as follows , find the sum of the convergent series :- see the equation as…

A: It is given that, ∑n=0∞25n     ...(1)   According to the sum of Geometric series, the sum of…

Q: in En"x" n=1

A: We have to find out

Q: is series to estimat e series be enough

A:

Q: If the series En=1 an converges absolutely, the sequence {b,} is bounded, then the series sin(a,)b,…

A: ∑ann=1∞ is absolutely convergent and bn is bounded .

Q: If the power series E anz" converges at 2i, prove that the series also converges at 1 – i.

A: Given : The power series  ∑n=1∞anzn  converges at z = 2i. To prove : We have to prove that the…

Q: What is the largest value of x for which the series (x – 11)" - n°5" n=1 is absolutely convergent?

A: This is a problem of series and sum calculation. Based on the formula and concept we will answer the…

Q: What is the limit as n goes to infinity of the power series (log n)2 ?

A: The given problem is to find the limit of n goes to infinity of the power series of the function…

Q: If a function f has a Maclaurin series, what are the possibilities for the interval of convergence…

A: Given: If a function f has a Maclaurin series, what are the possibilities for the interval of…

Q: The series E² is convergent and has a sum.

A:

Q: Is the series 4k convergent? What is the easiest way to answer this question? Can you tell if 3* xp…

A:

Q: Which amongst the following is required to find mode in continuous series?

A: Let f1 be the highest frequency number fo be the frequency just preceding highest frequency number.…

Q: In (5–x)

A:

Q: The divergence test applied to the series 4k (7k + 9)* tells us that the series converges.

A: Given: Here,              ak=4k(7k+9)3≈4k73k3=473k2=bk(say) Now,                 limk→∞ akbk=limk→∞…

Q: In the root test if p>1 than the series is diverges O True false

A: In this question, we need to find whether the given statement is true or false.

Q: If an alternating series (-1)"a, satisfies lim, 00 an = 0, then it converges %3D Select one: O True…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 00 (-1)" Ln-1 n п — n=2

A:

Q: f (x) = (1+4x)?

A:

Q: If the lim, (1+)" =e, then the series a, is (i) Converge (i) Diverge (ii) Inconclusive (1)

A: we have given that limn→∞1+1nn=e

Q: Find an easy expression for the sum of the series on its interval of convergence. (-1)"-'n -x" 2"…

A: Given series is ∑n=1∞-1n-1n2nxn

Q: Let L = lim |an]/n The series an n=1 converges if

A:

Q: For what value of r does the infinit Series Sn Convergent

A: Given data÷

Q: If it is known that limk00 ak = 0 , that is the kth term of a series goes to zero as k goes to…

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Q: The series E,= is convergent. Select one: O True O False

A:

Q: If the series an , and E (an + b,) are convergent series then b, may be a divergent series. Select…

A:

Q: Suppose that > an(x+9)" converges at a = 13. At which of the following values of x must the series…

A: Consider the given information.

Q: Find both the interval and radius of convergenceof the Power Series るt Show!

A:

Q: If aN is the nth digit in the decimal expression of 1/3, is the series convergent or divergent?…

A: According to the given information, An is the nth digit in the decimal expression. So, for the…

Q: Show that the series 71 n' (2n)! is convergent. Deduce that lim 0% (2n)! n=1

A: We have to show that the series ∑n=1∞nn2n! is convergent. Let an=nn2n! Now,…

Q: Find the sum of the convergent series tan - ( m til tan M=1

A: This is a telescoping series.  Whose sum is  2/π

Q: Find the sum of the following convergent series: Eltan-(2n – 1) – tan(2n + 3)]. n=0

A: Given series ∑n=0∞tan-12n-1-tan-12n+3 Assume ∑n=0∞tan-12n-1-tan-12n+3=∑n=0∞an-∑n=0∞bn Where…

Q: Give an example of two convergent series E1 *k and E1 Yk such that = *kYk diverges. Can this happen…

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Q: If an converge to zero then the series -0 an is convergente Select one: True False

A:

Q: Find the radius and interval of convergence, R, of the series. En-1 2n

A: For radius of convergence we have to findlimn→∞an+1an<1  in the form of x<RAnd radius of…

Q: 3. Suppose that the following alternating series converges. (-1)" n2" Determine the number values…

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Q: п En-)" sin (-1)" 2

A:

Q: Find the sum of the series for the values of x, for when the series converges.

A:

Q: If Ea,x" converges on the interval [- 10,10], where does the series a, (2x - 2)" converge?

A: The Series converges on [-4,6].

Q: If Ea, is a convergent series of positive terms, prove that Esin (a„) converges.

A:

Q: State what it means for a series to be absolutely convergent. As well, if >Ja, converg * (2n +1) 1..…

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Q: If an alternating series (-1)"a, satisfies lim, 00 an = 0, then it converges

A:

Q: Consider the series , ark1, a 0. Then if r < 1, the series converges to

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Q: If a series (-1)" n=1 is convergent, then it is absolutely convergent. Select one: True O False

A: Given that  If a given series is convergent then it is absolutely convergent.

Q: The value of limx→o ex-1-x x² by using series is

A: I have given the answer in the next step. Hope you understand that

Q: If a power series in (x – 4) converges when x = 11, then it must also converge when x = -2. |

A:

Q: s of convergence

A: Here we have to find the radius of convergent,  we have,

Q: Consider series E-1 an 00 n=1

A: