Monday, January 11, 2010

1/11/09 Angus

First we reviewed how we used Gauss' method to find the n term of an arithmetic sequence. Then we went over a proof of why this method works. The proof was described by Mr. O'b. as follows,
Sn=a_{1} +(a_{1}+d)+(a_{1}+2d)...+(a_{1}+(n-3)d)+(a_{1}+(n-2)d)+(a_{1}+(n-1)d)
Sn=a_{n} +(a_{n}-d)+(a_{n}-2d)...+(a_{n}+(n-3)d)+(a_{n}+(n-2)d)+(a_{n}+(n-1)d)
2Sn=(a_{1} +a_{n})+(a_{1} +a_{n})+(a_{1} +a_{n})+...(a_{1} +a_{n})+(a_{1} +a_{n})+(a_{1} +a_{n})
2Sn=n(a_{1} +a_{n})
Sn=\frac{n}{2} (a_{1} +a_{n})
Then we went over homework questions that were difficult. Then began going over our notes on a geometric sequence. We defined a geometric sequence as follows,
Recursive:
a_1

a_n=r\cdot a_{n-1}
Closed Form:
We also came up with an equation for the sum of the n terms of a finite geometric sequence.
We also went over a proof for this, which when canceled, gives you this formula. We also defined an equation for the sum of an infinite sequence,
If , then

Here is the review for the midterm: midterm exam revision guide


HW

  • Sequences and Series revision sheet
  • Be prepared for a homework quiz covering all Unit 4 homework, including revision sheet (time to ask questions before the quiz). The first question on the quiz will be to write down the 5 formulas: closed form for arithmetic/geometric sequences, sum formula for arithmetic/geometric/infinite geometric (these are the boxed formulas on the two half-sheets).
  • Organize Unit 4 homework to be submitted by 2:15 Friday.


Posted by at
Labels: , ,

No comments:

Post a Comment

Subscribe to: Post Comments (Atom)