For which of the following series does the alternating test ensure convergence? D[(-1)" In ² (cos - -) n=1 Pi n=1 )(−1)” arctan(7n) Σ(-1)" I "+1 n n=1 Σ(-1)" n=1 Σ(-1)" n=0 1 )(−1)" arctan = n n=1 2n - 1 2n + 1 n=1 3n 1 (-1) (3-¹)" Σ(-1)", (−1)n (n!) ² (2n)! n=0 [(-1)" (¹²) " 5 n=0 n Σ(−1)n (n²)! n=0 (2n)!

Q: the power series ∞ (7-2x)" Consider f(x) = Σ function. 6n n=1 as a a. Find the interval of…

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Q: : Use the Comparison Test to verify if the following series is convergent or divergent: 2" sin (5n)…

A: Given :  ∑n=0∞2nsin25n4n-cos2n=∑n=0∞an  Now 0≤sin25n≤1 ⇒0≤2nsin5n≤2n   ∀ n∈ N             (1)…

Q: Match the following power series on the left column with the correct radius R of convergence on the…

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Q: In which of the following options are the power series representation of the function f(x) x3 and…

A: Given a function fx=x32-x2 and we have to find the power series representation of the given…

Q: (1) Find the radius and the interval of convergence of the power series. Be sure to check the…

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Q: Consider the following four series A =(2x)", B = E(2.r)", C= (-1)" (2x)", D = (-1)" (2.x)*" n n=1 n…

A: As you asked multiple sub part I only solved first three sub parts

Q: Determine whether each of the following series is convergent or divergent using the appropriate test…

A: Note:- Here given series are varies from n equal 1 to infinity  If given series varies from 1 to n…

Q: Which of the following series is divergent? Vn2 +1 5n2 +n n=1 In(n) n=2 1 Σ n(Inn)2 n=2 n2 3" n=1

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Q: Consider the power series (-1)^x^ n=1 9m (n²+4) M8 interval of convergence gues From x = to x =…

A: Ratio test -: If a series ∑n=1∞anxn is given and  limn→∞an+1an=L if L<1,then series converges…

Q: Which of the following series diverge? = N/W 2 K² +1 1. Z K=05K² +7 I. II. Ex-2(-1)*(x²+4) m. ΣΧ.…

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Q: (1) Find the radius and the interval of convergence of the power series. Be sure to check the…

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Q: 7n-1 Consider the power series: > (п — 5)3 6" n=1 First apply the ratio test to find L and then use…

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Q: Given the Maclaurin series for cos x : (-1)" -2²n COs x = (2n)! n=0 (i) Find the Maclaurin series…

A: Ratio test to find interval of convergence

Q: 2.1 Consider the power series E an(z – 2+ 3i)2". n=0 (a) If 0 < L < oo is the radius of convergence…

A: Ans : Let R be a radius of convergence of given series Formula 1/R = lim | a(n+1)/a(n)|   as n tend…

Q: Consider the power series E an(z - 2+3i)2". n=0 (a) If0 < L< oc is the radius of convergence of the…

A: Consider the given series ∑n=0∞anz-2+3i2n. (a) Let 0&lt;L&lt;∞ is the radius of convergence. We know…

Q: Find the interval of convergence for the following series: J'(x)2n-1 n3n n=1

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Q: π.χ. COS(TEX) 3 f(x) = 7 cos

A: f(x)=7cos⁡(πx3)

Q: Find the interval of convergence for the following series: S(x– 2)" n² · 3n | n=1

A: The given series is  ∑n=1∞x-2nn2.3n The standard form of series is  ∑n=1∞anx-an and the radius of…

Q: Σ Зп - 2, 5n' -8 4. 3. 3

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Q: Consider the power series ∑∞n=0 an(z - 2 + 3i)2n. (a) If 0 < L < ∞ is the radius of convergence of…

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Q: Find the interval of convergence of the series. Sn=00 (z-8)" n=1 n+8 O -1 < x < 1 O - <z < -00 <x<…

A: We ahve to find the interval of convergence of the series.…

Q: 6.7 what s the interval of con vergence for the following power series ? (メ-2)" 8" n' n-1

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Q: Match each of the Maclaurin series with the function it represents. 00 x" 1. п! n=0 00 (-1)"x²n 2.…

A: Using Maclaurin series formula we get:

Q: Find the Maclaurin series for sin(x?). Select the correct answer below: 2n+1 E(-1)", (2n + 1)! n=0…

A: Maclaurin Series can be written as -  F(x) = F(0) + F'(0) x + (F''(0) x2 /2!)+........ Given F(x) =…

Q: D n In (1+ n=1 n16 arctan E 5" In (1+ > sin n=1 2n+1 n=1 F

A: We have to choose the convergent series according to the given options