Problem 73
Question
What is the meaning of the symbol \(\Sigma ?\) Give an example with your description.
Step-by-Step Solution
Verified Answer
The symbol \(\Sigma\) in mathematics represents 'sum'. It is used for expressing the sum of a series. For example, the sum of integers from 1 through 4 using \(\Sigma\) notation would be \(\Sigma_{i=1}^{4} i = 1 + 2 + 3 + 4 = 10\).
1Step 1: Explanation of Symbol
In mathematics, the uppercase Sigma \(\Sigma\) is used to represent the 'sum' of a sequence or series. This sum is achieved by adding up all the terms present in the series.
2Step 2: Using Sigma Notation
When using \(\Sigma\), the general format is \(\Sigma_{i=a}^{b} f(i)\). Here, \(i\) is the index of summation; \(a\) and \(b\) are the lower and upper bounds of the sum, respectively; and \(f(i)\) is the function to be summed.
3Step 3: Examples
For example, in the expression \(\Sigma_{i=1}^{4} i\), sum all integer numbers from 1 (the bottom number, or \(a\)) through 4 (the top number, or \(b\)). The value of this expression is 1 + 2 + 3 + 4 = 10.
Other exercises in this chapter
Problem 73
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