19.1. Summation Notation
To find the sum of a series of numbers, such as the sum of the first ten even numbers or 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20, we use a formula denoted by sigma (Σ). If the series begins at n = 1, the function that describes the series is 2n such that 2(1) = 2 at n = 1, 2(2) = 4 at n = 2, 2(3) = 6 at n = 3 until we reach 20 at n = 10. It can be written as:
The uppercase Greek letter sigma (Σ) tells you to take the sum of the expression beginning at n = 1 which is written below the sum. The sum is evaluated until n = 10 which is written on top of the sum. In order to find the sum, first find the value of the expression at each n and add them together to get 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 = 110.
Finding a Sum
1) Go to the Greek keyboard next to the a-z button.
2) Tap the arrow above the 0-9 key to switch to uppercase letters and select Σ.
3) Tap the 0-9 keyboard to go back to the default keyboard.
4) Enter the upper and lower limits in brackets. Separate the values with a comma.
5) Enter the expression. If it is longer than one term, close it in parentheses, e.g. x^2 - 2x or 4x + 5.
Finding a Sum
1) Go to the Greek keyboard next to the a-z button.
2) Tap the arrow above the 0-9 key to switch to uppercase letters and select Σ.
3) Tap the 0-9 keyboard to go back to the default keyboard.
4) Enter the upper and lower limits in brackets. Separate the values with a comma.
5) Enter the expression. If it is longer than one term, close it in parentheses, e.g. x^2 - 2x or 4x + 5.
Illustrative Example
Find the given sum.
Examples
Find the given sum.
Find the given sum.
Calculator solutions
a) Type sigma ( Σ ) by going to the Greek keyboard.
b) Tap the up-arrow key, then select sigma ( Σ ).
c) Switch back to the 0-9 keyboard to enter the expression.
d) Enter the upper and lower limits in brackets. Type brackets by tapping the parentheses keys twice. Type the variable either by using the x variable key or by using the a-z keyboard. Separate the limits by using a comma.
c) Enter the expression of the sum in parentheses.
Enter the sum using the following syntax: Σ[x = 3, 10](x^2 + 2x)
Enter the sum using the following syntax: Σ[x = 1, 7](3x^2 - 2)
Enter the sum using the following syntax: Σ[k = 1, 7](4k^3 - 2k^2 + 5)
Enter the sum using the following syntax: 5Σ[x = 1, 5](4x^2 - x + 1)
Enter the sum using the following syntax: 3Σ[x = 1, 5](2x + 3) - 4Σ[y = 1, 3](2y - 1)
Type y by tapping the x variable key twice.
Type y by tapping the x variable key twice.
