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
2 1/2x−34(2x+5)=3/8 what id X ?
Phantasy [73]
2 because I looked it up on google
3 0
3 years ago
A function and its inverse are shown on the same graph. Which statement describes the relationship between the function and its
Korvikt [17]

Answer:C

Step-by-step explanation:on edge

5 0
3 years ago
0.719 rounded to the nearest hundredth
lapo4ka [179]

Answer:

0.72

Step-by-step explanation:

hope i helped

pls mark brainliest im trying to level up

4 0
3 years ago
Read 2 more answers
Alyssa said that 6/8 and 9/12 are not equivalent because there is no whole number you can multiply both part of 6/8 by to get 9/
BigorU [14]

Solution: Alyssa is incorrect.

In fact \frac{6}{8}=\frac{9}{12}.

If we cross-multiply the above equation, we have:

6 \times 12 = 9 \times 8

72 = 72

Therefore, they are equal.

Also, if we reduce the given fractions, we have:

\frac{6}{8} =\frac{3}{4}

And

\frac{9}{12}=\frac{3}{4}

Since both the fractions reduced to \frac{3}{4}, therefore fractions are equivalent.

7 0
3 years ago
If you flip a coin or roll a 6-sided die, what is the probabilty that you will flip a tails and roll a 2?
telo118 [61]

Answer:

\frac{1}{12}

Step-by-step explanation:

P(tail) = \frac{1}{2}

P(2) = \frac{1}{6}

P(tail and 2 ) = \frac{1}{2} × \frac{1}{6} = \frac{1}{12}


3 0
3 years ago
Other questions:
  • PLS HELP ME ASAP FOR 12 and 13!!! (SHOW WORK FOR BOTH!!!) + LOTS KF POINTS!!
    8·1 answer
  • What is the volume of a right circular cylinder with a radius of 4 m and a height of 4 m?
    14·1 answer
  • PLEASE HELP THIS IS DUE TODAY!!
    15·1 answer
  • How do you find the intersection between 2 lines?
    5·2 answers
  • 40% of 80 percent of a quantity
    6·2 answers
  • HELP ASAP. BRAINLIST IF YOU ANSWERED IT RIGHT
    10·2 answers
  • Would love some help
    14·1 answer
  • Select the correct answer.
    6·1 answer
  • 10. The figure below is a uniform cross-section of a hall 20 m long and 7 m wide.
    12·1 answer
  • Ski shop made 80,000 profit this is 250 precent of last year’s profit
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!