Let's start from what we know.

Note that:

(sign of last term will be + when n is even and - when n is odd).
Sum is finite so we can split it into two sums, first

with only positive trems (squares of even numbers) and second

with negative (squares of odd numbers). So:

And now the proof.
1) n is even.
In this case, both

and

have

terms. For example if n=8 then:

Generally, there will be:

Now, calculate our sum:



So in this case we prove, that:

2) n is odd.
Here,

has more terms than

. For example if n=7 then:

So there is

terms in

,

terms in

and:

Now, we can calculate our sum:




We consider all possible n so we prove that:
Answer:
it would be 140
Step-by-step explanation:
Answer and explanation:
Geometary software is merely a software implementation of solving the area of a triangle. Therefore geometry software employs all the methods used in coordinate algebra(manual) albeit behind the scenes, in the console of the software, and just displays the area in the screen after solving. While geometry software displays the area using automated methods in code, coordinate algebra solves area of the triangle manually using several steps. In both cases, we observe that algebra is required to solve area of the triangle as it is part of the algorithm used in the code for the geometry software. Also being able to use the geometry software requires that one understand coordinate algebra to be able to plot lines, points and planes at the correct locations on the screen and get desired result.
12Sqrt(3)
This is because we can find the height and base of the triangle by using 30-60-90 triangles. Because the center point bisects the 60 degree angles in each corner, we can make 30-60-90 triangles. Then using porportions, you'll find the height of the triangle is 6 and the base is 4sqrt(3). Then use the area of a triangle formula.
Answer: D. 20
Step-by-step explanation:
(4/5)(25/1)
= 100/5
=20