What is a summation statement?

A summation statement, also known as a summation, is a mathematical notation used to represent the sum of a series of numbers. It uses the Greek letter sigma (Σ) to indicate the sum.

Here's how a summation statement is structured:

Σ (expression) [lower limit, upper limit]

* Σ: The Greek letter sigma, representing the summation operation.

* (expression): The expression or formula that determines the terms being summed. This expression typically involves an index variable.

* [lower limit, upper limit]: These define the range of values for the index variable. The lower limit is the starting value, and the upper limit is the ending value.

Example:

Let's say we want to find the sum of the first 5 natural numbers (1, 2, 3, 4, 5). We can represent this using a summation statement:

Σ (i) [i=1, i=5]

This means:

* Σ: Sum of the following expression.

* (i): The expression is simply the index variable 'i'.

* [i=1, i=5]: The index variable 'i' starts at 1 and goes up to 5.

To calculate the sum:

1. Substitute 'i' with each value from 1 to 5: 1 + 2 + 3 + 4 + 5

2. Calculate the sum: 15

Therefore, Σ (i) [i=1, i=5] = 15

Key Points:

* Summation statements are powerful tools for concisely representing and calculating sums of series.

* The index variable can be any letter (usually 'i', 'j', or 'k').

* The expression can be any mathematical formula involving the index variable.

* Summation statements are commonly used in calculus, statistics, and other areas of mathematics.

Let me know if you would like to see more examples or have any further questions.