Use of Summation Notation

Summation Notation Basics

The symbol for summation notation is the Greek capital letter Sigma (Σ).
It is often used to represent the sum of a sequence or series of numbers.
The general form of a summation is Σ (from j=a to b) of f(j) where a and b are the lower and upper bounds of the summation respectively.

Summation Properties

Commutative Property: The order in which the terms are added does not change the sum.
Associative Property: Grouping the terms in different ways does not change the sum.
Distributive Property: The sum of a series multiplied by a constant is equal to the sum of each term in the series multiplied by the constant.

Working with Summation

You can split a summation into multiple smaller summations if required.
You can interchange the symbols or indices as long as you maintain consistency.
Be familiar with the formulas to calculate the sum of natural numbers, squares of natural numbers and cubes of natural numbers as they are frequently used.

Calculation of Sum using Summation Notation

When calculating the sum of a series, replace the variable with the numbers from the lower limit to the upper limit and add the results.
To calculate the sum of an arithmetic series using summation notation, use the formula s = n/2 (a + l) where ‘n’ represents the number of terms, ‘a’ is the first term and ‘l’ is the last term.
For a geometric series, the sum can be calculated using the formula s = a(1 - r^n) / (1 - r) where ‘a’ is the first term, ‘r’ is the common ratio and ‘n’ is the number of terms.

Practice

Regular practice is key for mastering summation notation.
Analyse and solve diverse problems to enhance understanding of summation notation.
Use past papers to practice applying the rules of summation notation in various contexts.