Summation Notation

Summation (Sigma) Notation

The sum of the first n terms of a sequence, represented by

1 is the lower limit of the sum, which is the starting input of a sequence

The i is the index of summation

The n is the upper limit of the sum, which is the final input of the sequence

Use the limits and equation to find the sum

Examples:

= 2(3) + 2(4) + 2(5) + 2(6) = 36

= (2(5²) + 5(5) + 2) + . . .

When sums become very large, like the second example, using a calculator is useful to find the sum

To solve a sum with a calculator, plug this in:

sum(seq(explicit formula, variable, lower limit, upper limit))

Now the example from above:

sum(seq(2x² + 5x + 2, x, 3, 6)) = 270

Series

The sum of the first n terms of the seque nce is called a finite series

The sum of all terms of an ongoing sequence is called an infinite series

Can have a finite solution if a fraction is raised to an exponent

Partial Sums

The sum of the first n factors of a sum

infinite series, solve for the 5th partial sum

Substitute 5 for n, then find the sum of the first 5 numbers