Find Limit of Xn as n Approaches Infinity

dannysaf · 2009-09-17T22:13:11+00:00

Consider the sequence [SIZE="3"]x[SIZE="1"]n in which [SIZE="3"]x[SIZE="1"]n = 1/2([SIZE="3"]x[SIZE="1"]n−1 + (3/[SIZE="3"]x[SIZE="1"]n-1) and [SIZE="3"]x[SIZE="1"]1 = a (a not equals 0). Find lim [SIZE="1"]n →∞ [SIZE="3"]x[SIZE="1"]n

Thread starter dannysaf
Start date Sep 17, 2009
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Limit

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The discussion revolves around finding the limit of the sequence defined by xn = 1/2(xn−1 + (3/xn−1)) as n approaches infinity, with the initial condition x1 = a (where a is not zero). Participants are asked to demonstrate their approach to solving the problem and identify where they encounter difficulties. Key points include the need to analyze the recursive formula and apply mathematical techniques to derive the limit. The conversation emphasizes the importance of showing work and reasoning in reaching a solution. Ultimately, the limit of the sequence as n approaches infinity is the focal point of the inquiry.

Sep 17, 2009

dannysaf

Consider the sequence xn in which xn = 1/2(xn−1 + (3/xn-1) and x1 = a
(a not equals 0). Find lim n →∞ xn

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Sep 18, 2009

quantumdude

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You need to show how you started the problem, and where you got stuck.

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