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:

Step-by-step explanation:
We have been given a graph of the function f(x).
Now we need to use that graph to find the equation of the graph and match with the correct choice from the give choices:




We see that graph has end points in opposite direction then the degree of polynomial must be ODD.
Available degrees are 3 and 4. Degree 3 is odd so it is choice B or C.
Only
satisfies the given points from graph.
Hence correct choice is
.
Area = length *width
102 = 17*w
w = 102/17 = 6
l=17
w=6
perimeter = 2l +2w
p = 2(l+w)
p=2*23
p = 46 cm
hope helped
Answer:
Force= Mass×Accelaraion
F=m×a
But as The unit of accelaration is given miles per hour and the SI is meters per second sqaure we have to convert 10mph to m/s²
Thus, we have 10mph = 4.47 meters per second square. (i converted using scientific calculator)
So now we have,
2000N= m×4.47m/s²
= 2000/4.47m/s²=m
= 447.42
Thus the mass of the object is 447.42 (i am not sure of units)
Let the side of one square be x.
The maximum perimeter will be when the squares will be lined end to end.
This will be:
x + 9x + 9x + x
= 20x
The perimeter of the figures formed will be less than or equal to 20x.