If xi < x2 are arbitrary real numbers and 1 Xn := 2 for n > 2, 3dn-1+ 3"n-2 show that {xn} is convergent. identify the limit.

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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If \( x_1 < x_2 \) are arbitrary real numbers and

\[ x_n := \frac{1}{3}x_{n-1} + \frac{2}{3}x_{n-2} \]

for \( n > 2 \),

show that \( \{x_n\} \) is convergent. Identify the limit.
Transcribed Image Text:If \( x_1 < x_2 \) are arbitrary real numbers and \[ x_n := \frac{1}{3}x_{n-1} + \frac{2}{3}x_{n-2} \] for \( n > 2 \), show that \( \{x_n\} \) is convergent. Identify the limit.
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