Use summation notation to express each of the following calculations:
a. Add 1 point to each score, then add the resulting
values.
b. Add 1 point to each score and square the result,
then add the squared values.
c. Add the scores and square the sum, then subtract
3 points from the squared value.
a. Σ(x + 1)
b. Σ(x + 1)^2
c. (Σx)^2 - 3
a. The summation notation for adding 1 point to each score and then adding the resulting values would be:
∑(score + 1)
b. The summation notation for adding 1 point to each score, squaring the result, and then adding the squared values would be:
∑(score + 1)^2
c. The summation notation for adding the scores, squaring the sum, and then subtracting 3 points from the squared value would be:
(∑score)^2 - 3
a. To express the calculation of adding 1 point to each score and then adding the resulting values using summation notation, we can let n represent the number of scores, and let S_i represent the i-th score. The summation notation for this calculation would be:
∑(S_i + 1)
where i starts from 1 and goes up to n. This notation represents adding 1 to each score and then summing the resulting values.
b. To express the calculation of adding 1 point to each score, squaring the result, and then adding the squared values using summation notation, we can use the same notation as before but with an additional square operation. The summation notation for this calculation would be:
∑((S_i + 1)^2)
where i starts from 1 and goes up to n. This notation represents adding 1 to each score, squaring the result, and then summing the squared values.
c. To express the calculation of adding the scores, squaring the sum, and then subtracting 3 points from the squared value using summation notation, we can define similar variables as before. The summation notation for this calculation would be:
(∑S_i)^2 - 3
where i starts from 1 and goes up to n. This notation represents adding the scores, squaring the sum, and then subtracting 3 from the squared value.