Lexi is going to the movies. She buys one ticket and one bag of popcorn and spends.a
1 answer:
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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:
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
And now the proof.
1) n is even.
In this case, both
Generally, there will be:
Now, calculate our sum:
So in this case we prove, that:
2) n is odd.
Here,
So there is
Now, we can calculate our sum:
We consider all possible n so we prove that:
Step-by-step explanation:
I'll do one for you.
Using the formula for turning exponents into radicals
where b is the base
This means that the numerator in the exponet form becomes the power under the radical in radical form and
the denominator in exponet form becomes the nth root in radical form.
For example 5,
That becomes in radical form
or if you want to write it using positive exponents
I'll do one more for you
For example 6,
That becomes in radical form