Listen to the music ...
the geometric sequences music ....
Intermezzo

Evan Ma - Sequences and Series
http://youtube.com/watch?v=M1WzkWy3n74

The Story of Young Gauss ...
Photo Source: Karl Gauss (1777–1855)
to be continued ...

SEQUENCE
SERIES

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 \"rank\" of the nth term
a is the first term in the sequence
d is the common difference

(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?

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 \"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

Find the value of:

Given a geometric sequence in which and , what is the value of ?