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
ruslelena [56]
3 years ago
13

Determine the first four terms of the sequence in which the nth term is a_n=(n+1)!/(n+2)!

Mathematics
1 answer:
Vilka [71]3 years ago
4 0

Answer: Choice B) 1/3, 1/4, 1/5, 1/6

=============================================

Plug in n = 1 to find the first term

a_n = ( (n+1)! )/( (n+2)! )

a_1 = ( (1+1)! )/( (1+2)! )

a_1 = ( 2! )/( 3! )

a_1 = ( 2*1 )/( 3*2*1 )

a_1 = 2/6

a_1 = 1/3

The first term is 1/3. Optionally you can stop here because only choice B has 1/3 listed as the first term, so this must be the answer. However, I'm going to keep going to show how to find the three other terms. This will help confirm why choice B is the answer, and it will be handy for those times when you aren't given multiple choice answers.

------------

Plug in n = 2

a_n = ( (n+1)! )/( (n+2)! )

a_2 = ( (2+1)! )/( (2+2)! )

a_2 = ( 3! )/( 4! )

a_2 = ( 3*2*1 )/( 4*3*2*1 )

a_2 = 6/24

a_2 = 1/4

The second term is 1/4

------------

Plug in n = 3

a_n = ( (n+1)! )/( (n+2)! )

a_3 = ( (3+1)! )/( (3+2)! )

a_3 = ( 4! )/( 5! )

a_3 = ( 4*3*2*1 )/( 5*4*3*2*1 )

a_3 = 24/120

a_3 = 1/5

The third term is 1/5

------------

Plug in n = 4

a_n = ( (n+1)! )/( (n+2)! )

a_4 = ( (4+1)! )/( (4+2)! )

a_4 = ( 5! )/( 6! )

a_4 = ( 5*4*3*2*1 )/( 6*5*4*3*2*1 )

a_4 = 120/720

a_4 = 1/6

The fourth term is 1/6

------------

The first four terms are: 1/3, 1/4, 1/5, 1/6, so that confirms why choice B is the answer.

You might be interested in
Neeeeed help please
Nikolay [14]
A nice riddle, mathematical riddle.

Assuming a turtle winning means the declared winner is the weaker one actually won over the stronger one.  In this context, the turtle winner is the one who has a lesser number of favourable votes.

The given rules for the points are as follows:
1. Point for the first choice must be greater than or equal to that of the second choice.
2. All points must be positive whole numbers.

Let's suppose we have Henry against Tim.
Henry is favourite of the voters and is the leading candidate, according to popular polls.
Tim is an excellent manipulator, sly, and everybody knows this.

On polling day, the vote count came out as follows (in point counts)

Henry      Tim
2              1
2              1
2              1
2              1
2              1
2              1
10            1  (Henry's own vote)
1          100  (Tim's own vote)
------------------
17        107  TOTAL POINTS

So Tim the turtle was declared winner of the race, and since everything was according to rule, even a recount of the votes did not change the results.

Be aware, voting by districts (instead of popular votes) also exhibits a similar problem.



3 0
3 years ago
Read 2 more answers
A pair of linear equations is shown below:
trapecia [35]
That would be option D

The y intercepts are 1 and 4 and the slope are -1 and 2.
5 0
3 years ago
Read 2 more answers
a thermometer measures temperature to the nearest 0.5 degrees celsius which measurement shows an appropriate level of precision
Alja [10]

The temperature which has best degree of precision would actually be the temperature reading which has similar decimal place with the error. So the best answer would have 1 decimal and from the choices given above, this would be:

 

16.0°C

<span> </span>

4 0
3 years ago
Macy is making a border out of strips of wall boarder placed end to end along the 12-foot wall in her room. Each strip is foot l
3241004551 [841]
The answer is 4 let's make a equation to answer it 3*y=12 we need to get y simply multiply 1*3=3 2*3=66 is half way so we can double 2 to 4  4*3=12 so y=4. you only need 4 boards to complete the wall.
4 0
3 years ago
Can someone explain the answer to this and how to work it
9966 [12]
Your answer is 3/5, the picture below shows how sin cos tan work!

5 0
3 years ago
Other questions:
  • Solve the following quadratic equation using the quadratic formula. Which of the following expressions gives the numerators of t
    7·2 answers
  • What is the area of this figure ?
    9·2 answers
  • Compare the fraction below. write is greater then or is less than: 7/12 5/12
    14·2 answers
  • Find the midpoint of (0,4) and (-4,-12)
    6·1 answer
  • Can some one help me pleases
    14·1 answer
  • What type of graph can show positive correlation, negative correlation, or no correlation?
    9·1 answer
  • Please help with algebra!!! ill give brainliest
    9·2 answers
  • I’m not sure if you can see it but please help me &lt;3
    14·1 answer
  • HELPPPPPP HELPPPPP ANYONE PLEASEEEEEEE
    14·2 answers
  • Help me pls thank you so much
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!