(-10)^n/(5n+3)*8^n+1,

Q: Does the series from n-1 to infinty of (-1)^n (1+(1/n))^n converge of diverge by the alternating…

A:

Q: Determine the interval of convergence of this power series: 1+ 2x + 3x² + 4x³ + 5x*+..

A:

Q: Determine the interval of convergence of the power series which is the sum from n=0 to infinity of…

A: Given :

Q: use n-th term test to test the series (-1)" +Jn-Jn

A: we have to test whether the given series is convergent or divergent

Q: Find the interval of convergence of the power series. (Be sure to ine your answer using set…

A:

Q: 4 n(n+1) nel

A: Given: ∑n=1∞1n(n+1)-4n

Q: The Interval of convergent for the series is: 4kk (a)[-4,4] (b)(-4,4] (c) [-4,4) (d)(-4,4)

A: The convergence of the series can be calculated using the convergence test. The ratio test is given…

Q: The series C,(x + 3)" converges at x = 2 and diverges at æ = -12. Based on this information, what…

A: Given series is ∑Cnx+3n converges at x=2 and diverges to x=-12 Since, at x=2 series converges Hence,…

Q: Σ Find the interval of convergence of the power series :

A: Interval of of convergence is the set of values of x for which the power series converges.…

Q: What is the remainder of a convergent alternating series whose sum isapproximated by the first N…

A: The remainder of the convergent alternating series is S-Sn. if the alternating series satisfy the…

Q: Use Integral Test to determine whether the series 1 converges or diverges. (n + 2)% n=1

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Q: Prove that the Sum of Convergent. Series is ungue

A: prove that sum of convergent series is unique.

Q: Use the Integral Test to determine whether the series 4 converges or diverges. n=2 n(Inn)*

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

A:

Q: 15) En=1 2n2 00 3n2-1

A: Given : Limit equation is given Where ,an = 2n2 / (3n2 -1)

Q: Determine whether the given series is convergent or divergent. Inn 2

A: The given series is: ∑n=2∞ ln nn

Q: 00 3" n iM³

A:

Q: Determine the interval of convergence of the power series which is the sum from n=0 to infinity of…

A: The interval of convergence of the power series which is the sum from n=0 to infinity The answer is…

Q: What is the interval of convergence of the power series nx". -? en n=1

A:

Q: Determine the convergence or divergence of the series. 2 arctan(n) n = 1 Σ converges O diverges

A:

Q: 2. Is it possible for a power series to be conditionally convergent at two different points? it.

A: Sum of the geometric series can be expressed as ∑n=0∞axn=a1-xas we know that test for absolute…

Q: Determine the radius of convergence and interval of convergence of the power series ∞∑n=0nxn.

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Q: If the power series an" converges for x = 2, it also converges for x = -2. n=1 Select one: True…

A:

Q: this series is ans. absolute convergent for x < divergent at x=0 none of these conditional…

A: I will use radius of power series and alternating series test.

Q: 5-1)"" (x-5)" n

A: Power series

Q: Ek(x-10)*

A:

Q: 1) Does the series described by (-1)"; converge?

A:

Q: How to determine if the series, converges or diverges using only the convergence test?

A:

Q: @ Find the first four nonzero term- of the Tay lor series for the function f(x)=_ centered at a=2.…

A:

Q: 4. Using the integral test determine whether the series is convergent tan-(n) 1+n?

A:

Q: 2. Expand 1 into a power series with center zero and determine the interval of 2 – 3x3 -…

A: We have to find the power series and determine the interval of convergence.

Q: . Prove that the interval of convergence of the series Σ (-1)*--," 71 1. is -1<r <1.

A: See the attachment

Q: Does the series from 1 to  infinity of ((5n^3+n^2-15)/(n^3+2))^n converge or diverge by the root…

A:

Q: 1 Express 3, as the sum of a power series with center zero. What is the region of 1-3z validity of…

A: Te power series of the given function about z=0 is  ∑ n=0∞3nzn  and validity  Region is…

Q: Determine the interval of convergenee for the series 2(-1)" (2x – 3)"

A:

Q: Let 2 (-1)** 'ak be a convergent alternating series with terms that are nonincreasing in magnitude.…

A: We have to find the upper bound for  error.

Q: Determine whether the series converges or diverges. 9- 2(-1)" Σ converges O diverges

A: solve the following

Q: Determine whether the series is convergent or divergent Σ nt +1

A:

Q: Does the series from 1 to infininty of (-1)^n(1+(1/n))^n converge or diverge using the alternating…

A:

Q: Does the series from n=1 to infiniity of (-1)^n(1+(1/n))^n converge or diverge using the alternating…

A:

Q: Find the sum of the convergent series.

A: The given series is a geometric series with common ratio less than one. So we can use formula for…

Q: Does the series from 1 to infinity of -(2k)/(k+1)^k converge or diverge using the root test?

A: Given

Q: The series from n=1 to infinity of n(n+4)/sqrt(n^3+5n^2.  Does it converge or diverge?

A: Take n2  common from the denominator and then go ahead

Q: Determine whether the series nl-3n converges or 42n diverges. Show all your work.

A: To find- series is convergent or divergent.

Q: Find the sum of the convergent series. Σ

A: The given convergent series is, ∑n=0∞-47n To find its sum.

Q: 7) Explain why the series converges or diverges: Ln =0 (Hint: Geometric Series)

A: Use Geometric series test which states that:         ∑ n=1∞arn converges if and only if…

Q: of the series

A: We have to find

Q: Suppose there is a power series centered at 4, with an interval of [1,7). What are the intervals of…

A: It is given that the interval of convergence of power series is [1,7] and center is 4. Note that : A…