Answer:

Step-by-step explanation:
You have to use the summation notation formula:

where k is the starting number, n is the ending number and f(k) is the function or the expression to be added.
In this case, you have the sum of the integer numbers from 1 to 1000. Therefore, k=1 and n=1000.
Now, you have to obtain the function f(k) which is the representation of the expression needed to obtain the correct result of the sum.
f(k=1) = 1
f(k=2)=2
f(k=3)=3 ...
You can notice that the value of k corresponds to te value of f(k) therefore f(k) = k
Replacing the values of k, n and f(k) in the formula:

Олшчлиомдыдмшщулоовоыщ:))
Answer (numbers needed in boxes, going from top to bottom):
1
-1
-3
3
Step-by-step explanation:
f(x) is another way of saying y. So, the table is asking, "when substituting these x values for the x's in the function, what does y equal?" So, to answer the question, substitute each x value into the equation and solve.
1) Start with the x value of 1. Substitute 1 for x in y = 2x - 1 and solve:

So, when x equals 1, y equals 1. Therefore, the first box on the top must be filled out with the number 1.
2) Do the same with the rest of the x values. Here are the steps to solve each one, going in order from the top towards the bottom:
x = 0

x = -1
x = 2

I hope this helps you
-[x+y=5]
-x-y=-5
x+4y=14
-x-y+x+4y=-5+14
3y=9 y=3 x=2