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# shop11 - Anthony Reverri Section 27 Workshop 11 This weeks...

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Anthony Reverri Section 27 Workshop 11 This week’s workshop asks us to show that the series converges. We will prove that the series converges by utilizing the limit comparison test. The limit comparison test states that if and , are increasing, and if where L is both finite and positive, then and will both have the same behavior when it comes to convergence and divergence. The first thing we need to do is define and and show that they are both positive. We will let be the series we are interested in an be a simpler series which is similar to . First: Now for : Since and are the “dominating” terms in the series we will compare a n with a term involving just and . They are both “dominating” because when n is at extremely high numbers, the other terms, , , and will be so small relative to and , it will be as if they are not there. Therefore, at extremely high values, will behave the same way as so we will use this as our . Conclusively:

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## This note was uploaded on 12/05/2011 for the course MATH 152 taught by Professor Sc during the Spring '08 term at Rutgers.

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shop11 - Anthony Reverri Section 27 Workshop 11 This weeks...

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