1. Aim: What is the summation notation?
Do Now: If an = n2 + n, find the sum of
a1 + a2 + a3 + a4 + a5
HW: p.260 # 4,8,10,12,13,16,18,20

2. The sum a1 + a2 + a3 + a4 + a5 is called a series
A series is the indicated sum of a sequence:
We can use the summation notation to present the sum of a sequence (series)
This notation means replace i by 1,2,3,4 and 5, and then add up the resulting values

3. Summation notation (or sigma notation)
Is read as
“the sum from i equals 1 to 5 of i2 + i ”
upper limit of summation
lower limit of summation
index of summation
The index doesn’t have to be i. Any letter can be used. Also, the index doesn’t have to begin at 1.

4. Summation notation for an infinite series is similar to that for a finite series. For example, for the infinite series shown earlier, you can write:
The infinity symbol,  , indicates that the series continues without end.

5. Find:
Evaluate:
Evaluate:

6. Write the series with summation notation
··· + 100
Notice that the first term is 5 (1), the second is 5 (2), the third is 5 (3), and the last is 5 (20). So the terms of the series can be written as:
ai = 5i where i = 1, 2, 3, , 20
The summation notation is

7. Write the series with summation notation.
Notice that for each term the denominator of the fraction is 1 more than the numerator. So, the terms of the series can be written as:
Where i = 1,2,3,4…
The summation notation for the series is

8. Write the series by sigma notation:c)