Thursday, 3/29: Although yesterday was somewhat "fractured" due to the academic pep rally, today we answered questions about arithmetic and geometric sequences and series and completed a worksheet on successive differences and this should be the answers.
Monday, 4/9: Plans changed and instead of completing the Power Series, instead we looked at some special series. Homework tonight is:
1) Have Parametric Egg Project ready to turn in tomorrow.
2) Complete the Power Series Worksheet that was assigned March 30 if you haven't already done that.
3) Complete the Special Series Worksheet that was handed out today.
Answers to the Special Sequences Worksheet: 1. (1 + sqrt(17))/2 2. 9 3. (1 + sqrt(33))/2 4. (27 + sqrt(53))/2
5. (-3 + sqrt(21))/2 6. 2 7. (3 + sqrt(13))/2 8. 5
Although we didn't have time to go over those answers, I believe that these are the answers to the harmonic worksheet.
Tuesday, 4/10: Today we discovered a beautiful relationship between trig and exponential functions. Although each class had different ideas, we all came to the same conclusions. Last year's synopsis is here. Here is a synopsis of your class discussions. The homework is to complete the second part (the conclusions) of the power series and to study for a quiz. This COULD be on your quiz:
Part I. Given a sequence:
A) Identify what type of sequence this is (arithmetic, geometric, harmonic, quadratic, Fibonacci, binomial*, other),
B) Write its nth term (recursively or explicitly),
C) Write its 50th (or whatever) term.
Part II. Given a series: (arithmetic, geometric, nested radical, nested fraction or super simple other)
Note:This may be written in summation notation.
A) If it is finite, find its sum. (arithmetic, geometric, nested radical, nested fraction or super simple other)
B) If it is infinite, does the series converge? If so, what to?
Part III. Insert means (geometric, arithmetic, harmonic).
Part IV. Work with sequences to solve problems. (Some cool application possibly or something I've forgotten like
the binomial* series )
Friday, 4/13: We took a quiz Wednesday, got an Interesting Sequence to investigate,and looked at Mathematical Induction on Thursday. Here are samples of the induction proofs. Today the Interesting Sequence tasks were due and the assignment this weekend is to complete an investigation of the Golden Ratio (phi). The reason I want you to do this is because several of you have asked how to find the explicit form of the Fibonacci sequence. Well here is a pretty decent explanation of that, but until you realize that the ratio of successive terms of the Fibonacci sequence converge to phi, you don't know why they assume that the Fibonacci sequence is related to a geometric one.
UPDATE: The test on sequences is Tuesday, 4/17 and there will an induction quiz on 4/18.
Tuesday, 4/17: The test was today and here is tonight's 3D Graphing review. Please spread the word. Also remember that your first induction quiz attempt is tomorrow.