Important question on sequences, math homework help

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pbnpupnyiva

Mathematics

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I need help correcting an answer to the important sequence question.  Can someone please show me how to make the corrections properly.  I prefer a typed response on the word document so I can read it clearly.  I need to see the work.  Thanks. 

week_3_discussion_question_answer_correction.docx

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Here is the question Let r be a real number š‘Ÿš‘› Show that the sequence (š‘†š‘› ) = ( š‘›! ) converges to 0 Here is the answer that we came up with Ratio test: If there exists an N so that for all n ļ‚³ N , an ļ‚¹ 0 and Limit nā†’ļ‚„ If L ļ€¼ 1, then Limit nā†’ļ‚„ ļƒ„a n a n+1 =L an converges r ( n +1) n! (n + 1)! = Limit nā†’ļ‚„ ļ‚“r (n) (n + 1)! r (n)! = r Limit nā†’ļ‚„ 1! (n + 1) = r ļ‚“0 = 0 As L ļ€¼ 1, Sn = rn converges to zero. n! Here is what the professor said was wrong with the answer You are on the right track, and you have used the right approach, and the "guts" of the proof are correct, but there are shortcomings. (1) What if r = 0? Does the ratio test apply? HINT: Division by 0 is undefined. Establish the r = 0 case separately. (2) What series are we talking about here? You say that the series converges. What series? Why is there a series involved in this problem? (3) Please state the ratio test carefully (currently your first line is not a sentence), and bear in mind what the conclusion should be, and state it correctly. Please refine your work and post as a new reply. Thanks! I need help fixing the answer
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