To determine the beginning index number in the given summation, we need to carefully examine the summation notation. The summation can be expressed as:
[tex]\[
\sum_{x=2}^5 (x^2 + 4x - 4)
\][/tex]
Here's a step-by-step approach to decode the notation:
1. Summation Sign (Sigma Notation): The symbol \(\sum\) represents the summation process, which means we will sum the values of the given expression over a range of values.
2. Range of Summation:
- The lower limit is indicated below the summation symbol which shows the starting point of our series. For our given problem, this is \(x = 2\).
- The upper limit is denoted above the summation symbol and represents the last value of \(x\) in our series. In this case, it is \(x = 5\).
3. Expression to be Summed: The expression \(x^2 + 4x - 4\) inside the summation symbol is the function we are summing over the specified range of \(x\).
The problem specifically asks for the "beginning index number." The beginning index number is simply the value where the summation starts, which is the lower limit of the summation range. According to our given summation:
[tex]\[
\sum_{x=2}^5 (x^2 + 4x - 4)
\][/tex]
The beginning index number is \(2\).
Thus, the beginning index number for the summation is:
[tex]\[
\boxed{2}
\][/tex]
