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Friday, June 02, 2006 

THURSDAY JUNE 1ST CLASS

Two weeks before the exam. This is how today’s class began. Mr. K discussed how the exam is going to take place, that we going to do two question in the mac lab. And correct me if I am wrong. He also said the question are based on "design and measurement" and "Sequences". If you missed today’s class, then you missed Mr. K dripping Words of Wisdom. I am going to share little of his dripping words of wisdom. He said " You can't just walk out of the class if you wanted to. To walk out of the class, you have to walk half the distance from the exit (door), then again half of that, then half of that. Etc.... it also got something to do with sequences. The second thing was an ordinary man and his donkey. mmm. I think I better keep the rest to myself. i have shared enough. To get more of Mr. K dripping words of wisdom comment on the blog page, or if you are Mr. K student ask him in class tomorrow. Ok lets get business started. The notes are as follows:

Sequences & Series

Sequence: an ordered list of numbers that follow a certain pattern (or rule).


Series: the sum of numbers in a sequence to particular term in the sequence.


Example: Given the sequence: 3, 6, 12, 24, 48, ............

the series S5 denotes the sum of the first 5 terms:

S1=3 thus we have the series:
s2= 3+6= 9 3,9,21,45,93...
s3=3+6+12=21
s4=3+6+12+24=45
s5=3+6+12+24+48=93


in general, Sn denotes the sum of the first n terms.



Arithmetic Sequence:


i) Recursive Definition: an ordered list of numbers. Generated by continuously add a value.
(the common difference). to a given first term.
ii) Implicit Definition: an ordered list of numbers in the list is generated by a linear equation.

Common Difference: (d) i) the number that is repeatedly added to successive terms in an arithmetic sequences.
ii) From the implicit definition it is the slope of the linear function.

To find the n^th term in an arithmetic sequence.

tn= t1 + ( n - 1 ) d tn is the n^th term
t1 is the first term.
n is the rank of the n^th term.
d is the Common difference.

Geometric Sequence:

i) Recursive Definition: an ordered list of numbers generated by continuously multiplying a given first term by a particular value (common ratio)

ii) Implicit Definition: an ordered list of numbers where each number in the list is generated by an exponential function.

Common Ratio: (r) i) the number that is repeatedly multiplied to successive terms in a given sequence.



Geometric Sequence:

ii) from the implicit definition it is the base of the exponential function.


to find the n^th term in a geometric sequence.


tn= t1 (r) ^(n-1) tn is the n^th term
t1 is the first term
n is the Rank of the n^th term.
r is the (common ratio).

just don't forget that you can't have a series without a sequence.



Convergence and Divergence

When |r| > 1 the sum of an infinite geometric series Diverges. i.e. grows without bound.

When |r| <>

** Reminder that after the exams we do have classes, and we also going to do a pod cast. Basically it is kinda interview, don’t get scared. it not another exam. Mr. K is going to ask us couple of question, actually two questions to discuss. 1. What is something you would wish you would do better.
2. What thing would remind you of this class, that’s going to help you in future, studies i.e. university, and finally any closing comment.




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