∑(x+y)

c. ∑(x+∑(y))
d. ∑x+ ∑y
e. ∑(x)+ ∑(y)*

what do each of these mean?
what's the differences?

top line

(1 + 2) + (3 + 4) = 10

= (1+3) + (2 + 4) = 10

associate property of addition d.

as for the rest

c. add y values 2+4 = 6
now 1 + 6 + 3+6 = 16 NO

e. sum of x values + sum of complex conjugates of y values?

Sorry Damon, I am confused can you elaborate?

and use a, b, c, d, e so I know what you are referring to?

This may help as well

X = {2, 2, 9, 5, 6}
Y = {4, 7, 12, 8, 9}

These equations involve summation notation, which is a way to represent the sum of a series of numbers.

Let's break down each equation:

a. ∑(x+y): This equation represents the sum of each individual value of (x+y). It means that you add up all the values of (x+y) in your series.

b. ∑(x+∑(y)): In this equation, the outer summation (∑) represents the sum of each individual value of (x+∑(y)). The inner summation (∑(y)) represents the sum of all the values of y. So, you first add up all the values of y, and then add that sum to each value of x in your series.

c. ∑x+ ∑y: This equation represents the sum of all the values of x added together (∑x), plus the sum of all the values of y added together (∑y). It means that you add up all the values of x separately, and then add up all the values of y separately, and finally, sum the two sums.

d. ∑(x)+ ∑(y)*: This equation is similar to the previous one, but it looks like there might be a typo with the asterisk (*) at the end. Ignoring the asterisk, this equation represents the sum of all the values of x added together (∑(x)), and then adding that sum to the sum of all the values of y added together (∑(y)).

In summary, the main differences between these equations lie in how the x and y values are combined and if they are summed separately or together. It's important to carefully read and understand the notations to correctly interpret the equations.