Use power series to show that 1 1 1 e =- + 0! +...** 2! 3! 4! 5! 6! 117

Q: 2k k! - Decide if this series converges or diverges Lk=1 (k+2)!

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Q: Find the Maclaurin series 15 of I 8 1+X

A: From the formula for maclaurin series we solve the given problem

Q: 3-27 Find the sum of the series 5n+1 n=D0 (A) 2 (B)- * (C) (D) 1 (E) O (A) O (B) O (C) O (D) O (E)

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Q: The power series 1+2 (x+4)+ 3 (r+ 4)2 + 4 (æ + 4)3+.. is centered at x = 1 O r = 4 O x = -4 O x = 0

A: We have to find the center of the power series  1+2(x+4)+3(x+4)2+4(x+4)3+.........

Q: What is the sum of this series?  20/3 + 10/3 + 10/6 + 10/12 + 10/24 + 10/48 + 10/96+...

A: We have to find the sum of the series

Q: If 2n +3 5n +8 then the series n = 1 is divergent Select one: O True O False

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Q: By writing the summation of the three power series E nCx" +EC„x"-2+ £G,"-, we obtaln: O None of them…

A: Here we will 1st convert every series in such manner that every one will have same power of x in…

Q: convergent serie 12) Find the sum of each 2 A) / + = + ( ² ) ² + ( ² ) ³ + ( ²1 ) 4 + ... ( - )^² +…

A: Let's find sum of given series.

Q: Express the series using sigma notation 6m + 3m + 0 + (-3m) + (-6m)... E-3bn +9b E-3bn – 9b E-3bn…

A: Use the expression form the summation form

Q: Find the sum of the series 1+ 4*2! + + 16-4! + 64*6! ....

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Q: The series E-, 2k (-1)*+1 is 'k% D = 1

A: Using comparison test to find type of series. If series of absolute term is divergent then series is…

Q: (n*+3n)" (4n +5)"

A: Use Cauchy's root test

Q: Question # 6 Which of the following is/are power series? x" 1. Enx - 1) III. n! I. A) I only B) II…

A: a general power series can be written as ∑an(x-c)n ie. power series is a function of x or polynomial…

Q: Find the sum of the series S. 3- 3 In(8) 3 (In(8))? - 3 (In(8))³ _ ... 2! 3!

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Q: (-1)*+1 is The series 2k = 1 2k

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Q: Prove that the sum of the series 1/2 , 1/4, 1/8, 1/16 .........to infinity

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Q: Find the sum of the series S. 2 - 2 In(6) + 2 (In(6))² - 2 (In(6)) 21 ² . 3! S = 7.

A: A detailed solution is given below

Q: Use Leibniz's method to find the sum of the series 2² +9² +16² +23² + ... +72² Suggestion: This is…

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Q: (3n)! 3 (n!)³ n=1

A: We can test the convergence and find the interval and radius of convergence.

Q: divergent: Select one: O True False ts) The following series is 8 Σ6- n=1 3 n-2

A: Given: ∑n=1∞6-35n-2

Q: find the sum of the series 6 (2n-1)(2n+1) 2₁ M=

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Q: a. Differentiate the series 1 + x + x² + ·.. + x" +.. х to obtain a series for 1/(1 – x)². b. In one…

A: Since there are multiple questions present and you have not specified which question to answer,…

Q: The series 2(- 1)"+1 converges n = 1 Select one: True

A: The given series is ∑n=1∞-1n+1

Q: Find the limit of the series (if exist) 1 -1 3/4 1/4 4/3 1/3 None WI

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Q: Find the sum of the series

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Q: Decide whether the given series are convergent or divergent. Show all your steps. (-4)3n a) 2n+1 n=1

A: Since you have asked multiple questions in single request.so we will be  answering only first…