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
Jet001 [13]
3 years ago
15

Find the radius of convergence and the internval of convergence:

Mathematics
1 answer:
o-na [289]3 years ago
5 0
You can use the root test here. The series will converge if

L=\displaystyle\lim_{n\to\infty}\sqrt[n]{\frac{(4-x)^n}{4^n+9^n}}

You have

L=\displaystyle\lim_{n\to\infty}\sqrt[n]{\frac{(4-x)^n}{4^n+9^n}}=|4-x|\lim_{n\to\infty}\frac1{\sqrt[n]{4^n+9^n}}

Notice that

\dfrac1{\sqrt[n]{4^n+9^n}}=\dfrac1{\sqrt[n]{9^n}\sqrt[n]{1+\left(\frac49\right)^n}}=\dfrac1{9\sqrt[n]{1+\left(\frac49\right)^n}}

so as n\to\infty, you have \left(\dfrac49\right)^n\to0, which means you end up with

L=\dfrac{|4x-1|}9

This is the interval of convergence. The radius of convergence can be determined by finding the half-length of the interval, or by solving the inequality in terms of |x-c| so that R is the ROC. You get

|4x-1|
You might be interested in
Please help me PLEASE PLEASE PLEASE PLEASE PLEASE
Aneli [31]

Step-by-step explanation:

rocket : 26 mpg

Glimmer : 484/18 = 26.89 mpg

cambria : 392/16 = 24.5 mpg

Avenger : 60/2 = 30 mpg

a. Avenger, has the highest mileage

b. cambria, has the lowest mileage

c. Avenger,Glimmer, rocket, cambria

7 0
3 years ago
Find y, at and tu I need help please help
lesantik [10]

Answer:

there is no picture... but i will try my best to help you if you post picture in another question

8 0
3 years ago
Read 2 more answers
What subsets of numbers does 8 2/3 belong to?
Ne4ueva [31]
By simplifying the number given which is 8 2/3, we get an improper fraction of 26/3. Also, when we try to divide 26 by 3, we get an answer of 8.6667, with 6 as a repeating number after the decimal place. Therefore, this number is an example of real and rational number. Thus the answer is the second choice. 
5 0
3 years ago
If the cost price of a bag is AED 2176 and its selling price is AED 2497 then find the profit
ICE Princess25 [194]

Answer:

321 AED

Step-by-step explanation:

2497 - 2176 = 321 AED

6 0
2 years ago
11 Points Math Please help fast!!!
Vesnalui [34]

Answer:

do you still need the answer

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • 6x + 3y = -6 2x + y = -2 A. x = 0, y = -2 B. infinite solutions C. x = -1, y = 0 D. no solution
    12·1 answer
  • Which statement about the angle measures is true?
    7·2 answers
  • PLEASE HELP! Which of the following is the best definition of a Linear pair of angles?
    8·2 answers
  • Select three ratios that are equivalent to 5:2
    11·1 answer
  • Find the difference.<br><br> $9.30<br> - 4.12<br><br> A) $4.22<br><br> B) $4.42<br><br> C) $5.18
    10·2 answers
  • Find the slope of the line that passes through (10,1) and (5,2) PLEASE DO A STEP BY STEP EXPLANATION i learn nothing from my tea
    13·2 answers
  • The ratio of mango ice cream to strawberry ice cream is 2 : 5 .Total no. of ice cream is 49.what is the no. of strawberry ice cr
    13·1 answer
  • I NEED HELP ASAP!
    12·1 answer
  • What is thousand more a thousand more one millón what the answer putos
    14·1 answer
  • Can someone help me with this math work my brain broke-
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!