Help smart peep with 5. And6

N is a positive integer

Murrr4er [49]

Part (1)

n is some positive integer. Let's say for now that n is even. So n = 2k, for some integer k

This means n-1 = 2k-1 is odd since subtracting 1 from an even number leads to an odd number.

Now multiply n with n-1 to get

n(n-1) = 2k(2k-1) = 2m

where m = k(2k-1) is an integer

The result 2m is even showing that n(n-1) is even

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Let's say that n is odd this time. That means n = 2k+1 for some integer k

And also n-1 = 2k+1-1 = 2k showing n-1 is even

Now multiply n and n-1

n(n-1) = (2k+1)(2k) = 2k(2k+1) = 2m

where m = k(2k+1) is an integer

We've shown that n(n-1) is even here as well.

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So overall, n(n-1) is even regardless if n is even or if n is odd.

Either n or n-1 will be even. If you multiply an even number with any number, the result will be even.

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Part (2)

n is some positive integer

2n is always even since 2 is a factor of 2n

2n+1 is always odd because we're adding 1 to an even number. The sequence of integers goes even,odd,even,odd, etc and it does this forever.

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Another way to see how 2n+1 is odd is to divide 2n+1 over 2 and you'll find that we get (2n+1)/2 = 2n/2+1/2 = n+0.5

The 0.5 at the end is not an integer, so there's no way that (2n+1)/2 is an integer; therefore 2n+1 is odd.

6 0

2 years ago

Tara watched a movie at 3:19. The movie she watched was 1:20 long. When was her movie over?

solniwko [45]

About 4:39.
Hope this helps~!
~{Isle of flightless birds}

4 0

3 years ago

Read 2 more answers

WHAT IS THE DIFFERENCE BETWEEN ARITHMETIC AND GEOMETRIC SEQUENCES AND SERIES'?

uysha [10]

A sequence is a set of numbers.
If the difference between two consecutive terms is constant, then the sequence is called arithmetic and the difference is called the common difference.
If the numbers in the sequence follow a pattern were the next term is found by multiplying by a constant called the common ratio, r, then the sequence is geometric sequence.

8 0

3 years ago

Use f(x)=-2x+5 to find x when f(x)=11

Damm [24]

When it asks this question, ultimately you want to plug 11 into x because its f(x). 11=-2+5.

Then you subtract 5 on both sides because of the opposite of addition is subtraction.

6=-2x

now divide on both sides

x=-3

3 0

2 years ago

Copy DEF to the line so that S is the vertex. This task will be complete when you have constructed an angle with vertex S that i

tino4ka555 [31]

Explanation:

There are numerous videos and web sites that can show you the process of copying an angle. Some are animated. The best we can do here is show you a diagram with instructions. Of course, your curriculum materials already provide that.

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1. Set the compass to a convenient radius. Use that to draw an arc through rays ED and EF, using point E as the center.

2. Without changing the compass setting, draw a similar arc using S as the center, making sure it crosses the line containing S and extends far enough to accommodate the following steps. (In the attached, we show a full circle, because the tool we used won't draw an arc with a specific radius.)

3. Mark the points where the arc crosses ED as G, and where it crosses EF as H. Mark the point where the arc crosses the line containing S as I.

4. Set the compass radius to the distance GH. Using I as the center draw an arc with that radius so that it crosses the one made in step 2. Call that intersection point J. (Again, we have shown a circle because of the limitations of the tool being used for our diagram.)

5. Draw ray SJ to complete the angle copy.

4 0

3 years ago