The story of Young Gauss. Arithmetic and geometric series.

1. 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:

2. The Story of Young Gauss ...
Photo Source: Karl Gauss (1777–1855)

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

8. 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