1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alex777 [14]
2 years ago
14

For an integer n ≥ 0, show that (n/2) - (-n/2) = n. Use greatest integer function

Mathematics
1 answer:
mars1129 [50]2 years ago
3 0

The greatest integer function returns the largest integer smaller than the number you provide it. That is, if <em>n</em> ≤ <em>x</em> < <em>n</em> + 1, where <em>n</em> is an integer, then the "greatest integer of <em>x</em>" is [<em>x</em>] = <em>n</em>.

• Let <em>n</em> be even. Then we can write <em>n</em> = 2<em>k</em> for some integer <em>k</em> ≥ 0. Now,

[<em>n</em>/2] = [<em>k</em>] = <em>k</em>

while

[-<em>n</em>/2] = [-<em>k</em>] = -<em>k</em>

so that

[<em>n</em>/2] - [-<em>n</em>/2] = 2<em>k</em> = <em>n</em>

<em />

• Let <em>n</em> be odd. Then <em>n</em> = 2<em>k</em> + 1 for some integer <em>k</em> ≥ 0. Every odd integer occurs between two even integers, so that

<em>n</em> - 1 < <em>n</em> < <em>n</em> + 1

or equivalently,

2<em>k</em> < <em>n</em> < 2<em>k</em> + 2

so that

<em>k</em> < <em>n</em>/2 < <em>k</em> + 1

It follows that [<em>n</em>/2] = <em>k</em>.

Similarly, if we negative the previous inequality, we have

-<em>k</em> > -<em>n</em>/2 > -(<em>k</em> + 1), or -<em>k</em> - 1 < -<em>n</em>/2 < -<em>k</em>

which means [-<em>n</em>/2] = -<em>k</em> - 1.

So we make the same conclusion,

[<em>n</em>/2] - [-<em>n</em>/2] = <em>k</em> - (-<em>k</em> - 1) = 2<em>k</em> + 1 = <em>n</em>

You might be interested in
Write an algebraic expression from the following
gavmur [86]

A: (x^2) + 2x

B: (3x)/(4+x)

C: (5-x) × 3x

4 0
3 years ago
PLS I RLLY NEED HELP I MIGHT GIVE BRAINLIEST Just pls help
Lena [83]

Answer:

y=3x-7

step by step explaination:

4 0
3 years ago
Read 2 more answers
What is ac? HELP PLSSS​
elena55 [62]
What is the context for the question if there is any?
4 0
2 years ago
Read 2 more answers
Help!!!!!!!!!!!!!!!!!!!!!!! Pleaseeeeee
klasskru [66]

Answer:

C) 43.96

Step-by-step explanation:

1. Use the formula to find the circumference of a circle whic is C= πR

2. First multiply the radius (7 in) by 2

3. 7 x 2 = 14

4. Then multiply 14 by 3.14

5. 14 x 3.14 = 43.96

5. There's your answer :)

Hope this helps :)

8 0
1 year ago
12 meters in 28 seconds as a unit rate
blondinia [14]
You divide and get 3/7 meters per second
6 0
2 years ago
Other questions:
  • On her math quiz, Sandra lost 8 points for incorrect answers, but she gained 5 points for a bonus question. What is the sum of t
    10·1 answer
  • Which would be included in a probability model for rolling a cube with faces numbered 1 through 6. Select all that apply.
    14·2 answers
  • A binomial probability experiment is conducted with given parameters. Compute the probability of x successes in the n independen
    11·1 answer
  • 3) Write an equation for the relationship between the number of rectangles (x) and the perimeter of
    10·1 answer
  • Find the greatest common factor of the<br>following monomials:<br>12b 40b4<br>​
    6·1 answer
  • What percent is 36 out of 90
    10·1 answer
  • The product of the polynomials (3x+2) and (-x to the third - 3
    5·1 answer
  • The area of a square photo frame is 100 cm^2 find the length of the photo frame
    15·2 answers
  • 2 ( n - 7 ) = 20<br><br> What is n?
    8·1 answer
  • Derwin purchased a computer for $598.95, software for $128.88, and a wireless mouse for $14.95. Derwin will make equal payments
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!