Which of the following statement is true for the Ratio Test? none of the others O The series is divergent if lim„-c0 %3! 2. O The series is divergent if lim„-→c∞ The test is inconclusive if dn+l = 0. lim,0 %3D The series is convergent if lim-00 = 00. 1/2

Q: 12. En Applying the ratio test to the series 5k-1 (k + 1)? . 4k ’ you would compute ak+1 lim k v00…

A:

Q: n n² 2" . Evaluate the the following limit. If it is infinite, type "infinity" or "inf". If it does…

A: the objective is to evaluate the limit and tell about the series using the ratio test.

Q: the limits if it exists, if it does not explain why. (1) lim ()" (ii) lim

A:

Q: 4h +3n ne whether the series converges or diverges. If it converges, find its sum. 11 n= 1 e correct…

A: We have to choose the correct answer from the given option

Q: (i) Let an Σ n cos A. Which test should be used? (enter upper case DCT for direct comparison test or…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: The interval of convergence of the power series (-1)*(x+2)" (n+1)422 OA -651s2. OB. None of the…

A: The given series is: ∑n=0∞(-1)n(x+2)n(n+1)422n...(1) Let, an=(-1)n(x+2)n(n+1)422n, n≥0

Q: 52.(a) Let the series an be defined by a₁ = 1 and an+1 3 + sin n √n 18 n=1 Use the Ratio Test to…

A:

Q: Does the series from 3 to infinity for (ln(n))/(ln(ln(n)) converge conditionally, absolutely or…

A:

Q: Find the radius of convergence (R) and the interval of convergence (I) of the power series. (If the…

A:

Q: What is the power series for f(x)= 2/1+7x ?

A: we have been given the function  f(x)=21+7x

Q: If x <-, then, for any real number r, the series 2 converges to (1+ 2x)". Select one: O a. True O b.…

A:

Q: 00 ·Ë (-1)^_²_ n=1 n +1 Does the series converge absolutely, converge conditionally, or diverge?…

A:

Q: 3. Build a power series with the interval of convergence [-1, 9). (Note: There are many possible…

A:

Q: (i) The area of a triangle is (basexheight). (ii) Compute the areas A1, A2, etc..., find a pattern…

A: We know, I = ∫04f(x)dx=A1+A2+A3+.....

Q: 2 n+n+1 3″(n+1) n=1² n, 2

A:

Q: The series 0 Cn (x+4)" converges for x = 0 and diverges for x = 3. Circle/indicate the correct…

A:

Q: Determine the convergence or divergence of the series. Σ 910 O converges O diverges Submit Answer 9.…

A: Step 1: solution Step 2: Step 3: Step 4:

Q: Consider the series 00 (-1)" n=1 Use the drop-down menus to complete the following statement. 00 00…

A:

Q: n +9 Consider the series > a, where a, = 4" n=1 Compute the limit: an+1 (Enter "infinity" or "inf"…

A:

Q: > an where a,, = In n Consider the series n=8 Compute the limit: an+1 lim (Enter "infinity" or "inf"…

A: apply ratio test

Q: _2. Which of the following series is divergent? 1 1 1 (α) Ση=12n-1 (b) En=1,3 (c) En=13 Σ n2 _3.…

A:

Q: O [(1+ v2)* k=0

A:

Q: (x - 4)" Consider the power series and choose the correct 3" n=0 options below. • The center of the…

A: In the question it is asked to find solution for the given series.

Q: the series Σ(-1)n-1 ln(n) n n=1 solutely convergent, conditionally convergent, or divergent? Make…

A:

Q: 00 7n + 1 Consider the series >( . Evaluate the the following limit. If it is infinite, type…

A: Answer

Q: 11. Series k=1 For each of the following sequences {a}, decide wether the series Σak is convergent…

A:

Q: edia of nl D to an els gaixixcos biguiz ayd dhe ofereb bas ellexitan This question concerns the…

A: This question is about series.

Q: Σαπ M n=1 an = Σ n=1 3n+n 6"+In(n) We want to use the limit comparison test to determine whether…

A: Step 1:  Here given series is ∑n=1∞​an​=∑n=1∞​6n+ln(n)3n+n4​ Step 2: Here noted that in numerator…