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fix: correct week12 Q3 convergence iteration count#5

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rwmath27:fix/week12-convergence-iterations
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fix: correct week12 Q3 convergence iteration count#5
rwmath27 wants to merge 1 commit into
kelvinfkr:mainfrom
rwmath27:fix/week12-convergence-iterations

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@rwmath27

@rwmath27 rwmath27 commented Jun 1, 2026

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Summary

  • Correct the answer hint for Week 12 exercise 3.
  • The original calculation used ln 10^6, but reducing the error from 100 to 0.01 requires 100 * 0.99^k < 0.01, i.e. 0.99^k < 10^{-4}.

Details

The correct threshold is:

k > ln(10^4) / ln(1/0.99) ≈ 916.42

Therefore the minimum integer number of iterations is 917, not 1380.

Verification

  • Checked the derivation from the exercise statement.
  • Ran a numerical sanity check for ceil(log(1e-4) / log(0.99)).

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