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
gayaneshka [121]
2 years ago
5

Determine whether the sequence converges or diverges. if it converges, find the limit. (if an answer does not exist, enter dne.

) an = n2 n3 5n
Mathematics
1 answer:
Arada [10]2 years ago
4 0

The sequence a_n=\frac{n^2}{n^3+5n} diverges.

For given question,

We have been given a sequence a_n=\frac{n^2}{n^3+5n}

We need to determine whether the sequence converges or diverges.

From given sequence we have, a_{n+1}=\frac{(n+1)^2}{(n+1)^3+5(n+1)}

We use Ratio Test.

According to Ratio Test, r=\frac{a_{n+1}}{a_n}, where sequence converges if and only if |r| < 1.

Consider,

\lim_{n \to \infty} |\frac{a_{n+1}}{a_n} |\\\\= \lim_{n \to \infty} |\frac{\frac{(n+1)^2}{(n+1)^3+5(n+1)}}{\frac{n^2}{n^3+5n}} |\\\\\\= \lim_{n \to \infty} |\frac{(n+1)^2(n^3+5n)}{n^2[(n+1)^3+5(n+1)]} |\\\\=\infty

Since \lim_{n \to \infty} |\frac{a_{n+1}}{a_n} | is not defined, the sequence a_n=\frac{n^2}{n^3+5n} diverges.

Therefore, the sequence a_n=\frac{n^2}{n^3+5n} diverges.

Learn more about the sequence here:

brainly.com/question/17175513

#SPJ4

You might be interested in
3600<br> in standard<br> form
slavikrds [6]

Answer:

3.6 x 10^3

Step-by-step explanation:

4 0
3 years ago
What are the factors of the expression (y-2)(x+3)?
masya89 [10]

Answer:

Something which is multiplied by something else. A factor can be a number, variable, term, or a longer expression

with this information we can conclude that the numbers  2 and 3 are factors

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
What are the prime factorization of 12 and 9
zaharov [31]

it will be 3.

Step-by-step explanation:

6 0
3 years ago
Solve: 3x^2+16x+5=0
ExtremeBDS [4]

Answer:

(3x+1)(x+5)

Step-by-step explanation:

Sorry for my handwriting lol hope this makes sense

6 0
3 years ago
Please help with my homework
Akimi4 [234]

Answer:

I've given you steps already, do it yourself

5 0
2 years ago
Read 2 more answers
Other questions:
  • How many solutions dose this system have ? <br> X+4y=6 <br> y=2x-3
    11·1 answer
  • How many four-digit personal identification numbers (PIN) are possible if the PIN cannot begin or end with a 0 and the PIN must
    13·2 answers
  • The number of students at Nicks school has 98% of last years number. Currently, there are 1,170 students. How many students were
    6·2 answers
  • 11.56 divided by 0.04
    5·1 answer
  • Beau buys a skateboard with a price tag of $82.50. The tax rate is 8%. How much does he pay, including tax
    11·1 answer
  • 2. Scale: 4 inches = 12 miles. If the drawing length is 13 inches, what is the actual<br> length
    11·1 answer
  • Can you help me in need help mad
    14·1 answer
  • Solve 4(x + 1) = 4x + 4.<br><br> a. No solution<br> b. 0<br> c. All real numbers<br> d. 1
    5·1 answer
  • A store display rotates 40 times every half hour. How many times will the display rotate in 4 hours?
    7·1 answer
  • 5&lt;2y&lt;12 where y is an integer.<br> Write down all the possible values of y.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!