Q2. For what values of x does the series (-)" (x - 3) +- (x - 3)2 + ...... + (x – 3)" + converge? What is its sum? What series do you get if you differentiate the given series term by term? For what values of x does the new series converge? What is its sum?

Q: Find the interval of convergence for the series below: 11"(포")(n + 1) (n + 4) n=1 The series is…

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Q: Find the radius of convergence and the interval of convergence of the series. n!x" 1.3.5 ... (2n –…

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Q: 3. Find the radius of convergence and interval of convergence of the series (3x + 2)" (a) n! n=1

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Q: Find the series radius and interval of convergence for what values of x does the series converge x"…

A: We need to find radius and interval of convergence.

Q: Σ (n:)? The radius of convergence of the series (x- 2)2 is equal to ........ n=1 3" (2n) !

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Q: 3n + 4 to determine if the series E - converges or diverges, ratio test fails n=15n3 – 1 Select one:…

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Q: Find the radius and interval of convergence of the series. (л — 2)" 6" In n n=2

A: Given series

Q: Q2.Use n-th term test to test the series: E (-1)" /n+ Jn-Vn. n-1

A: To find- Use n-th term test to test the series: ∑n=1∞ -1nn + n - n     Test used-  The n-th term…

Q: Find the radius of convergence and interval of convergence of the series. n°r" (-1)" 4" R = I =

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Q: Suppose that > Cnx" converges when x = -4 and diverges when x = 6. What can be said about the…

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Q: Q2. Find the convergence interval and radius of the series: √n (2x+5)* nal

A: Given ∑n=1∞nn2x+5n

Q: 1. Find the radius of convergence and the interval of convergence for the power series. 1, (x+ 3),…

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Q: OnF Q7) Find the convergence interval and radius of the series: En=0 no

A: We find Radius of Convergence by using Root Test.

Q: ...+ 2 (i). For what values of x, does it converge? (ii). If you integrate the series term-by-term,…

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Q: 5. Find the radius and interval of convergence for the power series Σ-ν 1) i=1

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Q: 00 (4-x)"· /n+5 9n · 7" n=1

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Q: (2 2 First find the sum of this Series: (-1)"b)" the valnes of x for which the given series…

A: ∑n=1∞-1n x-1n3n=∑n=1∞-1nx-13n=∑n=1∞13-x3nFirst term (a) =13-x3,  common ratio (d)=13-x3Sum of the…

Q: 6) Find the radius and interval of convergence for the series E0 (x+3" 'n%=2 (n-1)2"

A: Given: The series is ∑n=2∞ (x+3)n(n-1)*2n

Q: Find the radius of convergence and interval of convergence of the series. 2n E(-1)" (5n)! R = ?v I…

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Q: 7. By using power series representations, find the function corresponding to given series E(-1)" "+2…

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Q: Find the radius of convergence and interval of convergence of the series. "+4 5n! n=2 R = I =[( +)-

A: We have to find R and I .

Q: (т — " 3) (-2)"/n n=1

A: I am going to find the radius of convergence and interval of convergence of the given power series…

Q: Find the radius of convergence and the interval of convergence of the series. (x + 4)" n² +1 n=1

A: ∑n = 1∞ (x + 4)nn2 + 1Series Ratio TestI6 limn→∞ 9n + 19n = LandL < 1, then ∑an…

Q: Find the radius of convergence and interval of convergence of the series. * 2" (x – 3)" n=0 'n +3

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Q: Find the radius of convergence and interval of convergence of the series. n=2 R = I =[[ +)

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Q: Given the series i). For what values of x, does it converge? (ii). If you integrate the series…

A: The given series is: ∑n=0∞-12n(x-7)n So, an=-12n(x-7)n So, L=limn→∞an+1an…

Q: Find the radius of convergence and interval of convergence of the series. 2n=1 2"(n²+1)

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Q: 13) Find the radius and interval of convergence of the power series (-2)" (x+3)" 3

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Q: For what values of x do the power series x" converge. n=1

A: The given power series is ∑n=1∞1+1nnxn. Consider an=1+1nnxn By using root test,…

Q: 3. Find the radius of convergence and the interval of convergence of the series 00 (-3)"x" Vn + 1…

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Q: Find the radius of convergence and interval of convergence of the series. Σ 3n! n=1

A: see 2nd step

Q: 12. Find the interval and radius of convergence of the series k=1

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Q: 10. Determine the interval and radius of convergence for the power series. 2k (x + 2)k k=1

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Q: n2 n=1 Using the alternating series error test, what is the least number of terms necessary to…

A: Given-              ∑n=1∞-1n+1n2 we have to find the least number to approximate the series.

Q: 6. Find the interval of convergence for the series E - (x+4)" n-2" n=1

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Q: (x + 2)" 8. 2n In n n=2

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Q: Find the interval of convergence and the ratio of convergence for the series Σ 3n(x-3)n/(n+3)!

A: Given  The series is ∑n=0∞3nx-3nn+3! .   Limit ratio test :- limn→∞an+1an=L if L <1  then ∑n=0∞an…

Q: 12. a) Find the range of values of x for which the series E1 (=) converges. c) Determine the value…

A: 12(a) Given infinite series is: ∑r=1∞x-3x-1r=x-3x-1+x-3x-12+x-3x-13+...... Let is consider,…

Q: 11) Find the radius and interval of convergence of (x + 3)" Σ the series n = 1 n!

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Q: Find the radius of convergence and interval of convergence of the series. (x – 4)" E(-1)" Зп + 1 n=0…

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Q: Find the radius of convergence and interval of convergence of the series. E(-1)": 3" n=2 R = I = [?…

A: Answer

Q: Find the interval and radius of convergence of the power series k -(x – 2)* 42k 1 k 1

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Q: 3. Find the radius of convergence and the interval of convergence of the series 00 (-3)"x" Vn +1 n=1

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Q: 11. Find the radius and interval of convergence of the series (x+2)" n4"

A: The solution are next step

Q: Find the radius of convergence and the interval of convergence of the power series. 4"(r – 1)" n=1

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Q: Find the radius of convergence and the interval of convergence of the series. Σ n 2 5n (x – 3)" n =…

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Q: 3. For the SERIES 2e ,determine whether it converges or diverges. If it converges, find n=0 the sum.

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Q: 12. Find the radius and interval of convergence of the power series ∞ n=1 (x-4)" √√3n

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Q: a, where a, = (-1)"+". n2 + 9 Consider the series n=1 Using the alternating series error estimation…

A: Given :-  Consider the series ∑n=1∞ an  where an =  -1n+5 nn2 + 9

Q: Find the radius of convergence and the interval of convergence of the series. (x+ 4)" n2 +1 n=1

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