Upcoming SlideShare
×

# Pre-Cal 40S Slides June 3, 2008

786 views
722 views

Published on

Arithmetic and geometric series.

Published in: Education, Technology
0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
786
On SlideShare
0
From Embeds
0
Number of Embeds
61
Actions
Shares
0
5
0
Likes
0
Embeds 0
No embeds

No notes for slide

### Pre-Cal 40S Slides June 3, 2008

1. 1. The Legacy of Karl Fredrich Gauss that is ... unstacking by ﬂickr user mikelietz Zehner by ﬂickr user threedots
2. 2. Some quot;quickiesquot; to get us started ... Find the value(s) of r in . In the geometric sequence, if = 3 and r = 2 , ﬁnd . If the ﬁrst term of a geometric progression is and the common ratio is -3, ﬁnd the next three terms. Determine the common ratio for the geometric sequence:
3. 3. http://www.sigmaxi.org/amscionline/gauss-snippets.html The Story of Young Gauss ... Photo Source: Karl Gauss (1777–1855)
4. 4. Series: The sum of numbers in a sequence to a particular term in a sequence. Example: denotes the sum of the ﬁrst 5 terms. denotes the sum of the ﬁrst n terms. Artithmetic Series: The sum of numbers in an arithmetic sequence given by is the sum to the nth term n is the quot;rankquot; of the nth term a is the ﬁrst term in the sequence d is the common difference
5. 5. Sigma Notation: A shorthand way to write a series. Example: means (2(1) -3) + (2(2) -3) + (2(3) -3) + (2(4) -3) = -1 + 1 + 3 + 5 =8 Σ is capital sigma (from the greek alphabet); means sum subscript n = 1 means quot;start with n = 1 and evaluate (2n - 3)quot; superscript 4 means keep evaluating (2n - 3) for successive integral values of n; stop when n = 4; then add all the terms (2n - 3) is the implicit deﬁnition of the sequence
6. 6. Introduction to today's class by Mr. Green on YouTube ... a summary of almost everything in this unit ... Sequences and Series on YouTube http://youtube.com/watch?v=WjLSz-nNLBc