Pre-Cal 40S Slides June 3, 2008

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