pre-cal 40s slides june 3, 2008
DESCRIPTION
Arithmetic and geometric series.TRANSCRIPT
The Legacy of Karl
Fredrich Gauss that is ...
unstacking by flickr user mikelietzZehner by flickr user threedots
Some "quickies" 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:
Photo Source: Karl Gauss (1777–1855)
The Story of Young Gauss ...http://www.sigmaxi.org/amscionline/gauss-snippets.html
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 termn is the "rank" of the nth terma is the first term in the sequenced is the common difference
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 sumsubscript n = 1 means "start with n = 1 and evaluate (2n - 3)"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
Sequences and Series on YouTube
Introduction to today's class by Mr. Green on YouTube ... a summary of almost everything in this unit ...
http://youtube.com/watch?v=WjLSz-nNLBc