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$₁ = 0.88 and Sn+1 = Sn+2 7 for n ≥ 1.

$₁ = 0.88 and Sn+1 = Sn+2 7 for n ≥ 1.

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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Use the Monotone Convergence Theorem to prove that the following sequences is convergent and then find the limit of the sequence.

 

The image presents a mathematical sequence defined as follows: - The first term of the sequence is given by \( s_1 = 0.88 \). - For subsequent terms, the formula is \( s_{n+1} = \frac{s_n + 2}{7} \) where \( n \geq 1 \). This sequence is recursively defined, meaning each term depends on the previous one. The formula indicates how each term is generated by adding 2 to the current term and then dividing the result by 7. This information can be used to calculate further terms in the sequence starting from the initial term \( s_1 \).
Transcribed Image Text:The image presents a mathematical sequence defined as follows: - The first term of the sequence is given by \( s_1 = 0.88 \). - For subsequent terms, the formula is \( s_{n+1} = \frac{s_n + 2}{7} \) where \( n \geq 1 \). This sequence is recursively defined, meaning each term depends on the previous one. The formula indicates how each term is generated by adding 2 to the current term and then dividing the result by 7. This information can be used to calculate further terms in the sequence starting from the initial term \( s_1 \).
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