Find the limit of a recursive sequence xₙ = ½(xₙ₋₁ + 3/xₙ₋₁)

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

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Start date Sep 17, 2009
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dannysaf

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Sep 17, 2009

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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quantumdude

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Sep 18, 2009

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

Find the limit of a recursive sequence xₙ = ½(xₙ₋₁ + 3/xₙ₋₁)

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