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Given the sequence defined recursively as • b =1 be is for every integer k>1 You will now use iteration to deduce a solution for this sequence: 1. Give the first 5 terms of the sequence. Show and keep the intermediate expansions because you will need them for the next step (and your grade will depend on it). 2. Based on this pattern. guess a non-recursive formula for the sequence that uses II or E. 3. Replace your series or product in the previous answer by a well-known formula in order to get an analytical solution for this sequence. a/z Hint: Note that for any non-zero x, can be simplified by multiplying the numerator and denominator by x. The pedagogical goal of this question is not to find an answer, but to learn how to use iteration to notice patterns in sequences, which is a more difficult skill. In order to do this, you must work from intermediate values instead of final values. Again, as for the previous question, do refrain from adding and multiplying everything because this makes patterns disappear.

Given the sequence defined recursively as • b =1 be is for every integer k>1 You will now use iteration to deduce a solution for this sequence: 1. Give the first 5 terms of the sequence. Show and keep the intermediate expansions because you will need them for the next step (and your grade will depend on it). 2. Based on this pattern. guess a non-recursive formula for the sequence that uses II or E. 3. Replace your series or product in the previous answer by a well-known formula in order to get an analytical solution for this sequence. a/z Hint: Note that for any non-zero x, can be simplified by multiplying the numerator and denominator by x. The pedagogical goal of this question is not to find an answer, but to learn how to use iteration to notice patterns in sequences, which is a more difficult skill. In order to do this, you must work from intermediate values instead of final values. Again, as for the previous question, do refrain from adding and multiplying everything because this makes patterns disappear.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Iteration #2 Given the sequence defined recursively as • bị =1 • b = for every integer k> 1 You will now use iteration to deduce a solution for this sequence: 1. Give the first 5 terms of the sequence. Show and keep the intermediate expansions because you will need them for the next step (and your grade will depend on it). 2. Based on this pattern. guess a non-recursive formula for the sequence that uses II or E. 3. Replace your series or product in the previous answer by a well-known formula in order to get an analytical solution for this sequence. a/z Hint: Note that for any non-zero x, can be simplified by multiplying the numerator and denominator by x. The pedagogical goal of this question is not to find an answer, but to learn how to use iteration to notice patterns in sequences, which is a more difficult skill. In order to do this, you must work from intermediate values instead of final values. Again, as for the previous question, do refrain from adding and multiplying everything because this makes patterns disappear.
Transcribed Image Text:Iteration #2 Given the sequence defined recursively as • bị =1 • b = for every integer k> 1 You will now use iteration to deduce a solution for this sequence: 1. Give the first 5 terms of the sequence. Show and keep the intermediate expansions because you will need them for the next step (and your grade will depend on it). 2. Based on this pattern. guess a non-recursive formula for the sequence that uses II or E. 3. Replace your series or product in the previous answer by a well-known formula in order to get an analytical solution for this sequence. a/z Hint: Note that for any non-zero x, can be simplified by multiplying the numerator and denominator by x. The pedagogical goal of this question is not to find an answer, but to learn how to use iteration to notice patterns in sequences, which is a more difficult skill. In order to do this, you must work from intermediate values instead of final values. Again, as for the previous question, do refrain from adding and multiplying everything because this makes patterns disappear.
Iteration #1 Given the sequence defined recursively as • aj =1 • an = n°an-1+1 for every integer n > 1 You will now use iteration to deduce a partial solution involving E and II operators for this sequence: 1. Give the first 6 terms of the sequence. Show and keep the intermediate expansions because they are more important than the final values for noticing a pattern. (and your grade will depend on it). 2. Guess a non-recursive formula which describes the sequence. The formula should include E and II operators and should be as compact as possible. The pedagogical goal of this question is not to find an answer, but to learn how to use iteration to notice patterns in sequences, and to write them correctly and succinctly using E and II notation. In order to do this, you must work from intermediate values instead of final values. Do distribute your operations to remove the parentheses in each term of the sequence, but do not calculate the results of additions and multiplications, because if you do the pattern will disappear.
Transcribed Image Text:Iteration #1 Given the sequence defined recursively as • aj =1 • an = n°an-1+1 for every integer n > 1 You will now use iteration to deduce a partial solution involving E and II operators for this sequence: 1. Give the first 6 terms of the sequence. Show and keep the intermediate expansions because they are more important than the final values for noticing a pattern. (and your grade will depend on it). 2. Guess a non-recursive formula which describes the sequence. The formula should include E and II operators and should be as compact as possible. The pedagogical goal of this question is not to find an answer, but to learn how to use iteration to notice patterns in sequences, and to write them correctly and succinctly using E and II notation. In order to do this, you must work from intermediate values instead of final values. Do distribute your operations to remove the parentheses in each term of the sequence, but do not calculate the results of additions and multiplications, because if you do the pattern will disappear.
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