S (0.9)" = 1 + 0.9 + 0.81 + 0.729 + ·

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 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 question as follows , find all values of x for which the series converges. For these…

A: Given: ∑n=1∞3xn

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 follows , use the Ratio Test to determine the convergence or divergence of…

A: given,        ∑n=1∞5n!

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 , find a geometric power series for the function, centered at 0,…

A: Given function is: fx=25-x We have to find the corresponding of f(x).

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: Use the ratio test to determine whether the series converges. If the test is inconclusive, then say…

A:

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

A: Let ∑n=1∞an=∑n=1∞-1n+1xn6n We will use ratio test'…

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

A: We have been given the series  ∑n=1∞ln nnn

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: In the given question as folows , verify that the infinite series diverges:- see the  equation as…

A: given: ∑n=1∞nn+1

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

A: Given series : ∑n=1∞sin2nn3

Q: Use the ratio test to determine whether the series converges. If the test is inconclusive, then say…

A: Given series:  ∑k=1∞k(1/5)k Then , ak=k(1/5)k ak+1=k+1(1/5)k+1

Q: (-1)" (х — 2)" 00 (п +1)* n=1

A: For the solution of the problem follow the next steps.

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

A: The ratio test is one of the tests to identify if the series is converging or diverging. In this…

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

A: The given sequence is ∑n=1∞(-1)n+1n43=∑n=1∞an where an=(-1)n+1n43

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

A: Given an alternating series, ∑n=0∞-1nn+4 To find the nature of the  series.

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

A: The given sequence is ∑n=1∞(-1)n+1n(5n+1)=∑n=1∞an Here an=(-1)n+1n(5n+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, find the radius of convergence of the power series:- see the…

A: Given,

Q: In (5–x)

A:

Q: In the given question as follows , find the radius of convergence of the power series, where c >…

A: Given :                  ∑n=1∞ (x-c)n-1cn-1 Formula :               By Ratio test, the series is…

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: (4-x)". /n 00 n+5 9n : 7" n=1

A:

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 , find the sum of the convergent series by using a well-known…

A: Find the sum of the convergent series by using a well-known function.              ∑n=0∞-1n12n+1

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: Use an appropriate test to determine whether the following series converges. 00 12 Σ 4. k=1 k

A: Definition: ∑k=1∞12k5=12∑k=1∞1k5=12∑k=1∞1(k)52 here p=52>1 this p is greater than 1 so using…

Q: state whether the series converges or diverges

A: Apply ratio test and check weather series is convergent or divergent.

Q: In  the given question as follows ,  determine the numberof terms required to approximate the sum of…

A: In  the given question as follows ,  determine the numberof terms required to approximate the sum of…

Q: In the given equation as folows, verify that the infinite series diverges. see the equation as…

A: Given : ∑n=1∞n2n+3

Q: In  the given question as folows , find the interval of convergence of the power series, where c…

A: Given series is  ∑n=0∞xkn=∑n=0∞xnkn where an=1kn.

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 given equation as follows , use the Ratio Test or the Root Test to determine the convergence…

A: Given series  1+23+332+433+534+635+... This can be written as 130+231+332+433+534+635+... So the…

Q: In the the question as attached here  find the radius of convergence of the power series:-

A: Here given series S=∑n=1∞4xnn2orS=∑n=1∞4nx nn2 Compare with ∑n=1∞anxn ⇒an=4nn2

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

A: Given: 1200+1400+1600+1800+........

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 follows , verify that the infinite series diverges:-   see the equation as…

A: Given: ∑n=1∞2nn2+1 To Determine: Series is Convergent or Divergent Concept: if limn→∞an≠0, then ∑an…

Q: In the given question as follows , verify that the infinite series diverges :- see the equation as…

A: Given:           ∑n=1∞nn+1 n(n+1) is the nth term of the series.…

Q: In the given question as follows , verify that the infinite series diverges :- see the equation as…

A:

Q: Use suitable test to determine whether the following series is convergent +00 e" sin(n!) n!

A:

Q: Use an appropriate test to determine whether the following series converges. 00 Σ 4 k = 1 V

A: Explanation of the answer is as follows

Q: Use the ratio test to determine if the series converges or diverges. Sn! n=1

A:

Q: Use any method to determine whether the series converges or diverges. VE 00 Σ k=1 + 27

A: