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Check: \(5^2 + 7^2 = 10^2\) - AMAZONAWS
Check: \(5^2 + 7^2 = 10^2\) - AMAZONAWS
📅 March 6, 2026
👤 scraface
Mar 06, 2026
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📌 We now verify that the sequence converges to 0. Note that \( G(t) = t(1 - rac{t}{4}) \). For \( t \in (0, 4) \), \( 1 - rac{t}{4} \in (0,1) \), so \( G(t) < t \) as long as \( t > 0 \). Since \( b_1 = 1 \in (0,4) \), and \( b_{n+1} = G(b_n) < b_n \), the sequence is positive and strictly decreasing. A bounded decreasing sequence converges. The only fixed point in \( [0,4) \) satisfying \( G(t) = t \) is \( t = 0 \). Hence:
📌 Time for second part = \( \frac{200}{80} = 2.5 \) hours.
