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:
6
Step-by-step explanation:
20 41 6
20 6 41
6 41 20
6 20 41
41 20 6
41 6 20
Answer:
3,131,313
Step-by-step explanation:
Let X represent the number of cases with diabetes in 1973.
An increase of 396% in diabetes cases in 1973 would be;
12.4 million = 396/100 × X
12.4 million = 396X/100
Cross multiply
12.4 million × 100 = 396X
X = [(12.4 million × 100) / 396]
X = 3,131,313
Therefore, the number of diabetes cases in 1973 is 3,131,313 cases
Answer:
Any value of "x" makes the equation true
Step-by-step explanation:
(-∞,∞)
All real numbers
i hope this work for you
Answer:
Step-by-step explanation:
multiply each side by 2
subtract 3 from each side
multiply each side by -1