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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

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nlexa [21]

Answer:

Savings = \frac{6.99}{50}\times 254.7 -  \frac{5.99}{50}\times 254.7 dollars.

Step-by-step explanation:

We are given that,

Juanita usually buys 50 pounds of mulch for $6.99.

That is, total cost of 254.7 pounds of mulch = \frac{6.99}{50}\times 254.7 dollars.

Now, since there is sale on the price of the mulch, we have,

Price of 50 pounds of mulch on sale = $5.99

Then, price of 254.7 pounds of mulch on sale = \frac{5.99}{50}\times 254.7 dollars.

Thus, the savings Juanita had = Original price of 254.7 pounds of mulch - Price of 254.7 pounds of mulch on sale.

Hence, savings = \frac{6.99}{50}\times 254.7 -  \frac{5.99}{50}\times 254.7 dollars.

3 0
3 years ago
Read 2 more answers
Plz, Help!!!!!!!!! Thank You
quester [9]
The second choice my dude
5 0
3 years ago
Pls help me with this, i’ll give brainly
Nataly_w [17]

Answer:

shirts = 15 when pants = 6

15

Step-by-step explanation:

Try two others that are given

shirts / pants = 10 / 4 = 2.5

shirts / pants = 30/12 = 2.5

So shirts/pants = 2.5 = x/6

2.5 = x / 6                            Multiply by 6

2.5 * 6 = x

x = 15

8 0
2 years ago
If the diagonals of a parallelogram are equal, then show that it is a rectangle.
Harlamova29_29 [7]

Answer:

Given: In parallelogram ABCD, AC=BD

To prove : Parallelogram ABCD  is rectangle.

Proof : in △ACB and △BDA

AC=BD  ∣ Given

AB=BA ∣ Common

BC=AD ∣ Opposite sides of the parallelogram ABCD

△ACB ≅△BDA∣SSS Rule

∴∠ABC=∠BAD...(1) CPCT

Again AD ∥ ∣ Opposite sides of parallelogram ABCD

AD ∥BC and the traversal AB intersects them.

∴∠BAD+∠ABC=180∘ ...(2) _ Sum of consecutive interior angles on the same side of the transversal is 

180∘

From (1) and (2) ,

∠BAD=∠ABC=90∘

∴∠A=90∘ and ∠C=90∘

Parallelogram ABCD is a rectangle.

4 0
2 years ago
There are 20 pieces of fruit in a bowl and 5 of them are apples. What percent of the fruit are apples?
Elodia [21]

Step-by-step explanation:

20fruits=100%

5fruits=?

5x100/20 5fruitsx5%

=24%

4 0
3 years ago
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