The Limit Comparison Test says that the series An and bn, with all an > 0 and b, > 0 either both n=1 n=1 an converge or both diverge if lim is .. bn O =c, where c is finite and positive. O =c where c is positive. O exists. O is not zero.

Q: 6) (④) f Z=1 f(2)-22-132-1) sangle single 2) 렇 2Tif(20) 2Tif (2) 32-1 f(x)= /3(일) 1 = 2 . . 2Ti(2) =…

A: Here we use Cauchy integral formula which states that if f(z) is analytic inside C and z = a is…

Q: can anything be said about E- an

A: Given that, ∑nan converges.

Q: 19. Give an example of divergent series E ak and E, bu such that the series E akbk converges.

A:

Q: an Q4. If £ an converges and an > 0 for all n , can anything be said about E- ?

A: Given that ∑an converges and an>0 for all n. The objective is to determine whether ∑1an converges…

Q: Use the Ratio Test to determine whether the series is convergent or divergent. 7 Σ k! k = 1 Identify…

A: Solution:-

Q: 2. Show that the series is conditionally convergent. n=2 cos(nx) √n ln n

A: Solution of the problem as follows

Q: Q2. Show that whether the following series converges or diverges n! n=1

A:

Q: a. Show that if two power series E-oa„x" and E-o b,x" are convergent and equal for all values of x…

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Q: 1. Prove that the p-series diverges for p < 1.

A: We have to show that  the p-series diverges for p&lt;1.

Q: Use the Root Test to determine the convergence or divergence of the given series or state that the…

A: Let us consider the series ∑n=0∞an Let us consider the limit function L=limn→∞an1n Root test, to…

Q: what is the radius high OF convergence of tar nower senes)

A: follow next step

Q: The series 00 1 + Vn? 1 + Vna n=1 is convergent if and only if: Select one: Oa. 72 a > Ob. 35 a 4…

A: (.)   The given series is ,                                                        ∑n=1∞1+n281+na7…

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

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Q: on whernn 0o then det ermine this series E2 an is Convergent or Divergent n=2 -3 b. En=2 n2+n n2-10…

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Q: 6 The series E is k=0 5k Converges to Diverges None 15 Converges to 2 이5

A: Given the series is ∑k=0∞65k Sequence will be converges if it has finite value. Sequence will…

Q: .2 .4 x + + 1 2! +... 3!

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Q: Which one of these sequences is convergent Select one: O a. none of these. Ob. 2n+9 n' nt О с. 2n+6…

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Q: For which z's does the infinite series 1+ 좋 + + +. zn + . 3" 27 converge? To what function does it…

A: The solution are next step

Q: 1.Does it follow that if an > 0 for all ne N, thenEn=1 an does not converge conditionally? Explain.…

A: We have to explain the given statement.

Q: Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is…

A:

Q: 10. Which of the following is/are correct? an is convergent. na n=1 I. For a = 2 the series II. For…

A: Option B is correct.