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
Leviafan [203]
3 years ago
10

Find the radius of convergence of the power series \sum_{n=1}^\infty \frac{x^n}{\root 9 \of n}

Mathematics
1 answer:
vesna_86 [32]3 years ago
5 0
Assuming "root 9 of n" is supposed to mean "the ninth root of n", that is \sqrt[9]n we can use the ratio test, which says the series converges whenever

\displaystyle\lim_{n\to\infty}\left|\frac{\frac{x^{n+1}}{\sqrt[9]{n+1}}}{\frac{x^n}{\sqrt[9]n}}\right|

We have

\displaystyle|x|\lim_{n\to\infty}\frac{\sqrt[9]n}{\sqrt[9]{n+1}}=|x|\sqrt[9]{\lim_{n\to\infty}\frac n{n+1}}=|x|

which means the radius of convergence for this power series is 1.
You might be interested in
Solve the inequality showing all steps needed to justify your answer. State your solution in interval notation
dybincka [34]
<span>Which two measures did the United States take to counter terrorism after the September 11 attacks?

</span>
5 0
3 years ago
A crew of highway workers paved 1/2 mile in 1/4 hour. If they work at the same rate, how much will they pave in one hour?
mote1985 [20]

Step-by-step explanation:

The easiest approach is to realise that one hour is 3 times longer than

20

minutes. The longer the time, the more they will pave.

2

15

of a mile, in 20 minutes, how much in 60 minutes?#

They will pave 3 times more.

2

15

×

3

1

=

6

15

of a mile

6

15

=

2

5

of a mile

You could also use the 'unitary method' where you find out how much they pave in ONE minute (divide by

20

) and them multiply by

60

to find how much in one hour.

Look at what happens:

2

15

÷

20

×

60

=

2

15

×

1

20

×

60

3

=

2

15

×

3

←

exactly the same maths.

=

2

5

4 0
3 years ago
Read 2 more answers
Your sister is getting married this summer and she has asked you to help her select a D.J.
ioda
So Dave charges 150 at first and then 10.50 per each hour, so if your sister has the party going for say "h" hours, then his total charges will then be 150 + 10.5h.

now, Marvin's Mobile Music charges 135 at first, but then is more expensive per hour is 15 bucks per each hour, so if she has a party for "h" hours, then his total charges are 135 + 15h.

now, let's check when they're both equal, at how many hours will they cost your sister the same amount.

\bf 150+10.50h=135+15h\implies 150-135=15h-10.5h&#10;\\\\\\&#10;15=4.5h\implies 15=4\frac{1}{2}h\implies 15=\cfrac{9}{2}h\implies \cfrac{15}{\frac{9}{2}}=h\implies \cfrac{\frac{15}{1}}{\frac{9}{2}}=h&#10;\\\\\\&#10;\cfrac{15}{1}\cdot \cfrac{2}{9}=h\implies \cfrac{30}{9}=h\implies \cfrac{10}{3}=h\implies 3\frac{1}{3}=h

so, 3 and a third of a hour, or 3 hours and 20 minutes, they both will cost your sister the same amount, so it wouldn't matter who's hired if the party is only 3 hours and 20 minutes long.

however, after that, the one with higher hourly rate, Marvin's, gets more expensive, and she's better off hiring the one with cheaper hourly rate.

now, you can just get some mp3s and some loud speakers and nevermind the  DJs and you do it, or she can do it, I have the macarena song if you need that one.
3 0
3 years ago
How do you write 3.25 in simplest form
dedylja [7]
3.25 would be 3 1/4 because,

Step 1: You would rewrite the decimal number as a fraction with 1 in the denominator. So, 3.25 = 3.24/1

Step 2: Multiply it by 1 to eliminate 2 decimals places, so multiply the top and bottom by 10^2 = 100
3.25/1 x 100/100 = 325/100
Step 3: Now you find the greatest common factor, also known as GCF, of 325 and 100 if it exits then you reduce the fraction by dividing both numerator and denominator by it. GCF = 25
3.25/100 divided by 25/25 = 13/4
Now you would simplify it to make a proper fraction getting your answer
3 1/4
Does that make sense?
7 0
3 years ago
Read 2 more answers
What is 27% as a fraction in the simplest
Norma-Jean [14]

Answer:

0.27

explanation

<u>27</u>

100

8 0
3 years ago
Other questions:
  • What number gives a result of -3 when 10 is <br> subtracted from the quotient of the number and 5?
    8·1 answer
  • I wanna know what is 42/24 simplified
    14·1 answer
  • An acidophilus culture containing 150 bacteria doubles in population every hour. predict the number of bacteria in 12 hours
    6·1 answer
  • Joanne buys a rectangular rug with an area of 35/4 square meters. The length of the rug is 7/2 meters. What is the with, in mete
    7·1 answer
  • in one baseball season peter hit twice the difference of the number of home runs Alice hit and 3. Altogether they hit 9,how many
    8·1 answer
  • Quadratic fort<br> Solve.<br> -6 + 3x – 9x2 = -16<br> Choose 1 answer:
    8·1 answer
  • The ratio 8:12 is equivalent to y:9. what is the value of y?​
    5·2 answers
  • Please answer whats on the screenshot for brainliest
    13·1 answer
  • Please help! I will give points for helpng.
    8·2 answers
  • El peso que cargan tres pick-ups están en la razón de 2:6:7, cuánto carga el pick-up más grande, si el pick up menor carga 1500k
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!