The Legacy of Karl
Fredrich Gauss that is ...
unstacking by ﬂickr user mikelietz
Zehner by ﬂickr user threedots
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:
The Story of Young Gauss ...
Photo Source: Karl Gauss (1777–1855)
Series: The sum of numbers in a sequence to a particular term in a
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
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
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
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
Introduction to today's class by Mr. Green on YouTube ...
a summary of almost everything in this unit ...
Sequences and Series on YouTube