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
mr Goodwill [35]
1 year ago
6

Determine if the sequence converges or diverges 8, 108, 208, 308, 408

Mathematics
1 answer:
PSYCHO15rus [73]1 year ago
5 0

Hello there. To solve this question, we'll have to remember some properties about convergence of sequences.

Given the following sequence:

\mleft\lbrace a_1,a_2,\ldots,a_n\mright\rbrace

If it is a finite sequence, then it converges to its last term, that is the lim sup (or greatest term of the sequence).

If it is infinite, then the sequence only converges if this limit exists and is equal to zero, that is:

\lim _{n\rightarrow\infty}a_n=0

With this, we'll be able to determine whether the following sequence is convergent or not:

S=\mleft\lbrace8,108,208,308,408\mright\rbrace

Since it is a finite sequence, we already know it converges.

The lim sup of this sequence is its largest term, in this case, 408, and we write:

\limsup S=408

If it was an infinite sequence, on the other hand, we would have to determine the general term a_n and see if the limit is equal to zero.

Notice that there is a pattern between the values: the difference between two consecutive numbers is equal to 100.

In other words, it is an arithmetic progression with ratio equal to 100.

This means that we can use the following formula:

a_n=a_1+(n-1)\cdot r

Where a_1 = 8 and r = 100, therefore:

\begin{gathered} a_n=8+(n-1)\cdot100 \\ a_n=8+100n-100 \\ a_n=100n-92 \end{gathered}

And taking the limit as it goes to infinity, we have that:

\lim _{n\to\infty}a_n=\lim _{n\to\infty}100n-92=\infty

That is, the limit is not zero (not even a real number), so the sequence would not converge.

You might be interested in
Convert to a mixed number 8/5
DerKrebs [107]

Answer:

The improper fraction 8/5 can be changed to the mixed number 1 3/5 by dividing the numerator (8) by the denominator (5). This gives a quotient of 1 and a remainder of 3.

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
Our soccer team lost 9 games this season. That was 3/8 of all they played. How many games did they play this season?​
iogann1982 [59]

Answer:

15

Step-by-step explanation:

3/8 = 9

9÷3= 3

the remainder of 3/8 is 5/8 so

5x3=15

4 0
3 years ago
How do you find the roots of this problem?
Sonja [21]
Simplifies the problem, you divide by a value which if plugged into x would equal 0. One example is dividing by (x-1) as x=1 results in 0
5 0
3 years ago
What is the lcm of 13 and 9​
telo118 [61]

Answer:

LCM = 117

Step-by-step explanation:1.  Find the prime factorization of 9. 9 = 3 x 3  2. find the prime factorization of 13. 13 = 13  3. Multiply each factor the greater number of times it occurs in steps 1) or 2) above to find the lcm:   3 x 3 x 13 = 117. Hope it helped.

8 0
3 years ago
I need help with math it easy but im a lil slow so help
Varvara68 [4.7K]

Answer:

22.5 is your answer

Step-by-step explanation:

5 0
3 years ago
Other questions:
  • Six more than fives times a number (x) is at least 21. I need an inequality.
    13·1 answer
  • Ulissa is making a birthday card and wants to put a border made of pink ribbon all the way around the front of the card. The car
    8·1 answer
  • Simplify the expression. 10h+6-5h+3
    15·1 answer
  • If f(x) = x2, which of the following describes the graph of f(x) - 5? A)The graph of f(x) - 5 is a vertical shift of f(x) = x2 f
    11·2 answers
  • Given: 2x + 3y= 6.<br>What is the y-intercept?<br>(0,3)<br>(2,0)<br>(0,2)<br>no intercept<br><br>​
    5·1 answer
  • Jordan flipped a coin 492 times. Which of the following would be a good estimate of the number of times the coin landed on heads
    11·2 answers
  • Voris made 80 cookies this week. She baked 4 less than three times the total she made last week. Which equation, when solved for
    11·1 answer
  • 21. 13/4 x 42/9 =<br> O<br> A. 132/18<br> B. 64/9<br> O<br> C. 77/18<br> D. 41/6<br> Worth 2 points
    15·1 answer
  • Why did they ban squatted trucks??
    9·2 answers
  • for an open interval (0,1) of a set a that is a subset of x belonging to real numbers, is a a closed subset?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!