when dealing with sigma notation, if i enclose my formula with parenthesis,does it make it different from a formula with no parenthesis? plz help, I saw this in regents prep webpage and I just didn't see any difference, but they say that the parenthesis changes the result.
extra parentheses are often useful when entering expressions online, as formatting is often rudimentary
The text formatting in printed material often makes the parentheses unnecessary
In any case, if the expression is unambiguous without the parentheses, they are unnecessary.
thanks!!!!
When working with sigma notation, enclosing a formula with parentheses can indeed make a difference in the result. The use of parentheses affects the order of operations when evaluating the formula.
Let's take a closer look at an example to understand this better. Suppose we have the following sigma notation:
Σ(i^2), where i ranges from 1 to 5.
Without parentheses, the formula would be evaluated as follows:
(i^2) would be calculated for each value of i, and then the results would be summed up.
For i = 1, (1^2) = 1.
For i = 2, (2^2) = 4.
For i = 3, (3^2) = 9.
For i = 4, (4^2) = 16.
For i = 5, (5^2) = 25.
The sum would then be (1 + 4 + 9 + 16 + 25) = 55.
Now, let's see what happens when we enclose the formula with parentheses:
Σ((i^2)), where i ranges from 1 to 5.
In this case, the formula within the parentheses is the same, but the parentheses affect the order of operations. Now, the exponentiation operation is done first, and then the results are summed up.
For i = 1, ((1^2)) = 1.
For i = 2, ((2^2)) = 4.
For i = 3, ((3^2)) = 9.
For i = 4, ((4^2)) = 16.
For i = 5, ((5^2)) = 25.
The sum would still be (1 + 4 + 9 + 16 + 25) = 55.
As you can see from this example, in this specific case, there is no difference in the result when using or not using parentheses. However, in more complex formulas, the use of parentheses can change the order of operations and potentially lead to different results.
So, it is important to pay attention to the presence or absence of parentheses in sigma notation, as it can make a difference depending on the specific formula being used.