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:
Ok so the original bill you full out is $32.00 in that box. and the next box put 15% of $32
5 : 3
D1 = 3km = 3000 m (1km = 1000m)
D2 = 1800m
Ratio of D1:D2
=3000/1800
=1000/600 (dividing by 3)
=10/6 (dividing by 100)
=5/3 (dividing by 2)
= 5 : 3
Answer:
Baking c cookies and dividing them evenly among 4 friends.
Step-by-step explanation: