4n2 – 1 n-1

Q: In the given equation as follows , determine the convergence or divergence of the series:- see the…

A: We have been given the series  ∑n=1∞(-1)nnln(n+1)

Q: In the given question as follows  determine the convergence or divergence of the series :- see the…

A: Given : The series is ∑n=0∞ 6nn+1 .

Q: In the given equation as follows , determine the convergence or divergence of the series:- see the…

A: Given ∑n=0∞-1n2n+1!

Q: In the given equation as follows, use the Direct Comparison Test to determine the convergence or…

A: Given series is  ∑n=1∞1nn2+1 where an=1nn2+1

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 the given equation as follows , determine the convergence or divergence of the series using any…

A: Given: ∑n=1∞n2n2+1

Q: In the given equation as follows , use the Root Test to determine the convergence or divergence of…

A: The given sequence is ∑n=2∞n(lnn)n=∑n=2∞an    (let) ⇒an=n(lnn)n

Q: In the given equation as folows , use the Root Test to determine the convergence or divergence of…

A: Given : ∑n=1∞3n+2n+3n

Q: In the given question as follows, determine the convergence or divergence of the series :- see the…

A: Given series : ∑n=1∞3nn3

Q: In the given equation as folows , use the Root Test to determine the convergence or divergence of…

A: The given series is ∑n=1∞1n-1n2n To find: Determine whether the series is convergent or divergent

Q: In  th given equation as follows , determine the convergence or divergence of the series and…

A: Given: ∑n=2∞ ln nn  To determine: The convergence or divergence of the series.

Q: In the given equation as follows , determine the convergence or divergence of the series using any…

A: Ratio test: If limn→∞ an+1an<1 then the series ∑n=1∞ an converges.

Q: In the given equation as follows,use the Direct Comparison Test to determine the convergence or…

A: Given: ∑n=1∞12n-1

Q: In the given question as follows, use the Direct Comparison Test to determine the convergence or…

A: Consider the series ∑n=1∞sin2nn3

Q: In the given equation as follows , determine the convergence or divergence of the series and…

A: Given, ∑n=1∞2n2n+12 To determine whether the above series is convergent or divergent.

Q: In the given equation as follows, determine the convergence or divergence of the series :- see the…

A: We have ∑ an diverges if an does not converges to 0. Consider ∑n=2∞ nln n. Now,

Q: 00 > sin(" n=1

A: We will use test of divergence here

Q: In the given equation as follows , determine the convergence or divergence of the series using any…

A: Ratio test for alternative term series: If limn→∞ an+1an<1 then the series ∑n=1∞ an converges.

Q: In the given equation as follows, use the Direct Comparison Test to determine the convergence or…

A: Given series : ∑n=1∞sin2nn3

Q: In the given equation as follows , determine the convergence or divergence of the series using any…

A: a) ∑n=0∞(-1)n(2n+1)!b) ∑n=1∞(-1)n(2n-1)!

Q: In the given equation as follows , determine the convergence or divergence of the series:- see the…

A: Given: ∑n=1∞-1n+1nn2+5 To Find: Whether given series is convergent or divergent Concept: Alternating…

Q: Determine whether the following series is convergent or divergent full solution pls and write what…

A: We have to determine whether the given series is convergent or divergent. Here we use Ratio test

Q: In the given equation as follows , determine the convergence or divergence of the series using any…

A: Given : ∑n=1∞2π3n

Q: In the given question as follows, determine the convergence or divergence of the series :- see the…

A: We have been given the series  ∑n=1∞tan-1(n)

Q: In the given equation as follows , determine the convergence or divergence of the series using any…

A: Given, can be rewritten as ∑n=1∞103n3=103∑n=1∞1n3

Q: In the given equation as follows , determine the convergence or divergence of the series using any…

A: Given : ∑n=1∞5n2n-1

Q: In the given equation as follows , determine the convergence or divergence of the series:- see the…

A: Given: ∑n=0∞ -1nn!  To determine: The convergence or divergence of the series.

Q: In the given question as follows, use the Direct Comparison Test to determine the convergence or…

A: ∑n=1∞1n3+1

Q: In the given question as follows, determine the convergence or divergence of the series :- see the…

A: Given : ∑n=1∞e-n

Q: In the given equation as follows , find the interval of convergenceof the power series. (Be sure to…

A: For a power series of the form ∑n=0∞anxn the radius of convergence is the value R such that series…

Q: In  the given equation as folows , determine whether the series converges absolutely or…

A: Given, ∑n=1∞-1nn! To find the nature of the series.

Q: In the given question as follows , determine the convergence or divergence of the series:-

A: The given series is the oscillating series since there is integer power on -1. Hence methods to…

Q: In the given equation as follows , determine the convergence or divergence of the series:- see the…

A: Given series is  ∑n=1∞-1nen where an=1en which is alternating series.

Q: In  the given question as folows , find the interval of convergence of the power series. (Be sure to…

A: Consider the series : ∑n=0∞2xn Find the interval of convergence. The series ∑n=0∞arn is a geometric…

Q: In the given question as follows , confirm that the Integral Test can be applied to the series. Then…

A: ∑n=2∞1nln n

Q: In  the given  equation as follows , determine the convergence or divergence of the series:- see the…

A: Given series is  ∑n=1∞sin2n-1π2 where an=sin2n-1π2

Q: In the given equation as follows , determine the convergence or divergence of the series using any…

A: Given: ∑n=1∞-1n3n-22n To Determine: Whether the given series is convergent or divergent Concept:…

Q: In the given question as folows, confirm that the Integral Test can be applied to the series. Then…

A: Integral Test Let f(x) is a continuous and positive function in the interval [k,∞) then If improper…

Q: In the given question as folows  determine the convergence or divergence of the series :- see the…

A: Given: ∑n=1∞1n+1-1n+2 To check the series is convergence or divergence

Q: In the given equation as follows, confirm that the Integral Test can be applied to the series. Then…

A: ∑n=1∞ 23n+5Apply the constant multiplication rule:  ∑c·an=c·∑an=2·∑n=1∞ 13n+5   Let N be a natural…

Q: In the given question as follows , determine whether the series converges absolutely or…

A: Given series is  ∑n=1∞-1n+1n+3 where an=1n+3 which is alternating series.

Q: In the question as follows , determine the convergence or divergence of the series :- see the…

A: Given : ∑n=0∞75n

Q: In the given equation as follows , determine the convergence or divergence of the series using any…

A: By alternative series test, an alternative series ∑n=1∞(-1)n+1 an with an≥0 converges if and only if…

Q: In the given question as folows  , determine the convergence or divergence of the p-series :- see…

A: Consider the given: P-series test:The p-series is given by-∑n=1∞1np=11p+12p+13p+⋯where, p>0 by…

Q: In the given equation as follows , determine the convergence or divergence of the series using any…

A: Given: ∑n=1∞100n To determine whether is convergence or divergence

Q: Find the radius and the interval of convergence of the following power series: (x – 5) Σ k-1

A:

Q: Consider the series defined as follows: 1 3n2 + 1 n=1 Determine the convergence or divergence of the…

A:

Q: Use the Comparison Test to determine if the following series converges or diverges. 00 1 Σ 5n2 + 3…

A: Given : ∑n=1∞15n2+3

Q: Use an appropriate test to determine whether the following series converges. 1 Σ k=2 (k– 1)²

A:

Q: Find the interval of convergence of the following power series: (-1)"x" n=1

A: Given : Power series ∑n=1∞-1nxnn To find : Interval of convergence of the given power series?