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Mathematics · Grade 12

Sequences, Series and Mathematical Reasoning

Learners prove statements about all natural numbers with mathematical induction, manipulate sigma notation, decide when an infinite geometric series converges and find its sum, expand powers with the binomial theorem and Pascal's triangle, and investigate the long-run behavior of sequences, including recursive ones.

  • 4 lessons
  • About 140 minutes
  • Sequences, series and reasoning check: 11 questions
  • Ways to answer: fill in the blanks, choose an answer, match pairs, type a number, put in order and sort into groups
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What learners will discover

  • Write and critique proofs by mathematical induction.
  • Evaluate finite sums in sigma notation and infinite geometric series, deciding when an infinite series converges.
  • Apply the binomial theorem and Pascal's triangle, explaining coefficients by counting.
  • Describe the limits of explicit and recursive sequences.

Lessons

  1. Proof by mathematical induction 6 steps3 practiceabout 38 min
  2. Sums and infinite geometric series 6 steps4 practiceabout 36 min
  3. The binomial theorem 5 steps3 practiceabout 33 min
  4. Where does a sequence go? 5 steps2 practiceabout 33 min
  5. Sequences, series and reasoning check 11 questions at the end

Keep exploring

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Guide for grown-ups