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Mathematical induction

Mathematical induction. 9 .4. Finite differences. When given a sequence that is neither arithmetic nor geometric, we can try to find finite differences. For example: 2, 5, 10, 18, 30, 47, 70,…. Finite differences.

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Mathematical induction

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  1. Mathematical induction 9.4

  2. Finite differences • When given a sequence that is neither arithmetic nor geometric, we can try to find finite differences. • For example: • 2, 5, 10, 18, 30, 47, 70,…

  3. Finite differences • If the first difference is constant, our terms are linear (an arithmetic sequence) • If the second difference is constant, our formula for general terms is quadratic • If the third difference is constant, our formula for general terms is cubic. • Generalize the formula, plug in known values, and solve the system for the unknown constants.

  4. Example • Find a formula for the nth term • 3, 5, 8, 12, 17, 23, …

  5. Example continued

  6. Example • Find • 1, 7, 15, 25, 37, 51, …

  7. Example Continued

  8. Sums of powers

  9. Find the sum

  10. Homework • Pg642 #45-59 odd

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