(2) Determine whether the following series converge. Rigorously justify your answers (using the convergence tests from the lecture). ∞ ∞ (a) Σ n 2n (b) n2+1 n! n=1 n=1 ∞ շո (c) Σ 1+2n n=0 (α) Σ ΣΣΣ (e) (-1)+1 +1 n=1 n=1 n! 1 (f) 3n+2' n=1 (2n)!*

Q: (– 1)"-1(2x+1)", What is the radius of convergence for the power series n=1 2 8.

A: we know that radius of convergence when n→limit∞an+1an=L<1

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A: Given: ∑n=1∞3x-2n3nn+312

Q: 3. Determine which of the following series converge: (a) ( d) Σ 50 + 2n n= n=1 n O n (e) n=1 (2n2 –…

A: Please note that according to guidelines only first 3subparts is solved.

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Q: Find the series' radius of convergence. (x - 5)n n25n n=0 0o, for all x O 5 O 10

A:

Q: 3. ( for ) Find the power series representation f(x) = Σen(x - a)" n=0 f(x) = = 1 about x=a=0. Also…

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Q: 6. For the function y = In (1-x), determine its a. Maclaurin Series expansion up to fifth degree. b.…

A:

Q: (iii) 2n ! n= 1

A: The series is given as  ∑n=1∞xn2n! Here an = xn2n!an+1 = xn+12(n+1)! By D Alembert's ratio test, we…

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A: Since you have posted multiple questions which are not interlinked i can do first question as per…

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A:

Q: (2) Determine whether the following series converge. Rigorously justify your answers (using the…

A: To determine the convergence of each series, let's apply various convergence tests:We can use the…

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A: We have to find interval of convergence of the given series:

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A: Due to Bartleby answering guidelines I have solved only first three Subparts of the given question.

Q: I could use some help for no.5

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Q: For what values of x does the series E-1 n=1 x21+3 12² converge?

A: