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Firlakuza [10]
2 years ago
9

Determine if the following infinite series converges or diverges

Mathematics
2 answers:
stiks02 [169]2 years ago
7 0

The series diverges by the comparison test.

We have for large enough k,

\displaystyle \frac{k^3}{k^4+10} \approx \frac{k^3}{k^4} = \frac1k

so that

\displaystyle \sum_{k=0}^\infty \frac{k^3}{k^4+10} = \frac1{10} + \sum_{k=1}^\infty \frac{k^3}{k^4+10} \approx \frac1{10} + \sum_{k=1}^\infty \frac1k

and the latter sum is the divergent harmonic series.

Mandarinka [93]2 years ago
6 0

Using limits, it is found that the infinite sequence converges, as the limit does not go to infinity.

<h3>How do we verify if a sequence converges of diverges?</h3>

Suppose an infinity sequence defined by:

\sum_{k = 0}^{\infty} f(k)

Then we have to calculate the following limit:

\lim_{k \rightarrow \infty} f(k)

If the <u>limit goes to infinity</u>, the sequence diverges, otherwise it converges.

In this problem, the function that defines the sequence is:

f(k) = \frac{k^3}{k^4 + 10}

Hence the limit is:

\lim_{k \rightarrow \infty} f(k) = \lim_{k \rightarrow \infty} \frac{k^3}{k^4 + 10} = \lim_{k \rightarrow \infty} \frac{k^3}{k^4} = \lim_{k \rightarrow \infty} \frac{1}{k} = \frac{1}{\infty} = 0

Hence, the infinite sequence converges, as the limit does not go to infinity.

More can be learned about convergent sequences at brainly.com/question/6635869

#SPJ1

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Genrish500 [490]

Problem 10

You are correct. The answer is choice C. The cm^3 notation represents cubic centimeters, which is a unit for volume. Think of a 1 cm by 1 cm by 1 cm cube.

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

Problem 11

This problem is a bit strange. She borrows money ($100) but then it says she earns $300 per day. It makes no mention of her paying that $100 back, or when it's due back. I'll just assume that she keeps the $100 for the 12 days.

If that assumption is correct, then she'll have y = 300x+100 dollars after x days.

Plug in x = 0 and you'll get y = 100. Plug in x = 12 and you'll end up with y = 3700. Therefore, the two points on this graph are (0,100) and (12,3700).

The only window that has y = 3700 in it is the interval -150 \le y \le 3700 while the other windows are too small. So only choice D is the answer here. In other words, you'll have "yes" on choice D, and "no" on everything else.

5 0
4 years ago
Please show work it’s due tommorow I will give 35 Brainly
SCORPION-xisa [38]

Answer:

Step-by-step explanation:Worked out on paper shown below

Also I recommended a online app called (it has wierd name but it’s helpful for algebra) mathpapa

Also I do math in pen so the last answer is messed up it’s 4c^2d and then the rest of the parentheses.Sorry for that.

5 0
2 years ago
Determine the function which corresponds to the given graph <br> the asymptote is x= -1
MissTica

Answer:

Can't answer

Step-by-step explanation:

6 0
3 years ago
The value of the exponent in (22)−5<br><br>is​
lyudmila [28]

Answer:

Let's calculate:

22-5

• Remove minus in the exponent and invert the base:

= (1/22)5

• Expand the multiplication:

= (1/22) * (1/22) * (1/22) * (1/22) * (1/22)

• Find your result:

= 1/5153632 ≈ 0.000000194038

3 0
3 years ago
Can someone help with this question?​
Marizza181 [45]
Nooooooo sorry. Can’t
5 0
3 years ago
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