infinite series presentations

Directions

Symbolically

• Given series.
• Write out first several terms.
• Choose appropriate test to apply.
  • Justify choice
    • Why is it the best choice?
    • Show that the series meets the conditions of the test.
  • Clearly demonstrate application of test to the series.
  • If possible, find sum and/or approximation with appropriate accuracy.
• If another series test may be used, apply it to support your result. Do this at least once.
• If no other test applies, choose at least two tests that may look like possibilities and explain why those test do not actually apply. (If appropriate, you may want to do this even if multiple tests do apply to your series. For example, an alternating series where the alternating series test fails, but both the n^th-term test and ratio test apply.)

Numerically

• Series Terms
  • Write out the first several terms.
  • Calculate decimal approximations for these terms. (Approximations should be accurate to at least three decimal places unless you need more to see the differences in the terms.)
• Partial Sums
  • Calculate at least the first TEN partial sums (S₀, S₁, S₂, . . . , S₁₀). You may want to program your calculator, use a spreadsheet, or use Mathematica to generate these terms and/or possibly more.
  • Consider the sequence {S_n}.
  • Discuss the behavior of {S_n}.

Graphically

• Graph the sequence {a_n}.
  (Note: This is not a continuous function. You may also graph f (x) where f (n) = a_n, if that helps illustrate your series.)
• Graph the terms of the sequence {S_n}.
• How does {S_n} relate to {a_n}?
• How does this connect to your symbolic and numerical methods?

Other

• Creativity?
  • Engage the class.
  • Make your presentation interesting.
  • However, “creativity” is not a part of the grade.
  • Also, no food (for now . . .)
• Please try to keep presentation to approximately 5 minutes.

Following Days

During Warm-Up time of next class day:

• Watch presentation
• Do self-critique
• Complete reflection.

TURN IN FOLLOW-UP NO LATER THAN ONE WEEK AFTER PRESENTATION.

   Presentation Forms - Teaching and Learning - Calculus C Home Page - Project Information

Grading - Series Presentations

Presenters: _____________________________ Per.:______Date:________________


_____(20 pts.) Symbolically

_____(5 pts.) Appropriate test with justification
_____(5 pts.) Accuracy in test application
_____(5 pts.) Clarity in test application
_____(5 pts.) Other tests

_____(10 pts.) Numerically

_____(5 pts.) Partial Sums
_____(5 pts.) Discussion (Accurate and Clear)

_____(15 pts.) Graphically

_____(5 pts.) Graph {a_n}
_____(5 pts.) Graph {S_n}
_____(5 pts.) Discussion (Accurate and Clear)

_____(15 pts.) Other

_____(5 pts.) Preparation and overall presentation quality
_____(5 pts.) Thoroughly and accurately answers questions
_____(5 pts.) Follow-up (Self-Critique and Reflection)

_____(60 pts.) Total

    Presentation Forms - Teaching and Learning - Calculus C Home Page - Project Information

Abby Brown - Torrey Pines High School