Arithmetic and geometric series.

1. The Legacy of Karl
Fredrich Gauss that is ...
unstacking by flickr user mikelietz
Zehner by flickr user threedots

2. Allan is one of 7 men and Brigit is one of 10 women who wish to be
chosen for the show The Greatest Mathematician. From this group, 4
men and 4 women will be chosen.
What is the probability that both Allan and Brigit will be among the 8
people chosen?
Briefly explain your calculations.

3. 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

5. To Find the nth Term In an
Arithmetic Sequence
t is the nth term
n
t = a + (n - 1)d a is the first term
n n is the quot;rankquot; of the nth term in the sequence
d is the common difference
Example: Find the 51st term (t51) of the sequence 11, 5, -1, -7, ...
Solution: a = 11 t51 = 11 + (51 - 1)(-6)
d = 5 - 11 t51 = 11 + (50)(-6)
= -6 t51 = 11 - 300
n = 51 t51 = -289

6. To Find the nth Term In a
Geometic Sequence
tn is the nth term
a is the first term
n is the quot;rankquot; of the nth term in the sequence
r is the common ratio

7. http://www.sigmaxi.org/amscionline/gauss-snippets.html
The Story of Young Gauss ...
Photo Source: Karl Gauss (1777–1855)

9. 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

10. (a) What is the sum of the integers from 1 to 5000?
(b) What is the sum of all multiples of 7 between 1 & 5000?
(c) What is the sum of all integers from 1 to 5000 inclusive that are
not multiples of 7?

11. Sigma Notation: A shorthand way to write a series.
Example:
4
∑(2n - 3) means (2(1) -3) + (2(2) -3) + (2(3) -3) + (2(4) -3)
n=1 = -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

12. Find the value of:

13. 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.
Geometric Series: The sum of numbers in an geometric sequence
given by
or
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