Download Lesson 12-4 Summation Notation

NAME: _____________________________________________________________
Algebra 2: Lesson 12-4 Summation Notation
DATE: _________________
Learning Goals:
1) What is summation notation? How can we evaluate the sum of a finite series given in
summation notation?
2) How can we write a series in summation notation?
Summation Notation

The summation of a specific number of terms of a sequence (a series) can also be
represented in a compact form, called summation notation, or sigma notation.

The Greek capital letter sigma,

Given a sequence
using the expression:
, is used to indicate a sum.
we can write the sum of the first
terms of the sequence
∑

It is read, “The sum of

Example:

from
to
.”
To write the terms of the series, replace n by the consecutive integers from 1 to 5, as shown
above.
Example 1: Write the sum without using summation notation. You do not need to find the sum.
∑
∑
∑
∑
Example 2: Write the sum without using summation notation, and find the sum.
∑
∑
)
∑(
∑
(
)
∑(
)
∑(
)
(
)
Example 3: Write each sum using summation notation.
Strategies:

See if sequence is arithmetic or geometric  if it is you can find the explicit formula for the
sequence

If the sequence is not arithmetic or geometric, try to look for other patterns

Look to see if numbers are “famous” numbers like perfect squares or cubes
a.
b.
c.
d.
( )
( )
( )
( )
Application of Summation Notation
Let
represent the sequence of integers giving the yardage gained per rush in a high school
football game
.
a. Evaluate ∑
b. Evaluate
∑
c. In general, if
. What does this sum represent in the context of the situation?
. What does this expression represent in the context of the situation?
describes any sequence of numbers, what does
∑
represent?