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
vodka [1.7K]
3 years ago
15

Find a power series representation for the function; find the interval of convergence. (Give your power series representation ce

ntered at x = 0.) f(x) = x 1 − x5Find a power series representation for the function; find the interval of convergence. (Give your power series representation centered at x = 0.) f(x) = x 1 − x5
Mathematics
1 answer:
Lera25 [3.4K]3 years ago
8 0

Answer:

1/5.

Explanation:

Note that the sum of infinite geometric series is equally to: a/ (1 - r). Where a = first term and r is the common ratio.

Hence, if f(x) = 3/(1 - 5x) ^2. Therefore, taking the another derivative of f(x)` = 30/ (1 - 5x)^3.

Also, f(x)`` = 450/ ( 1 - 5 )^4 and f(x)``` = 9000( 1 - 5x)^5 and f(x)```` = 225000/( 1 - 5x)^6.

If we are to use the Taylor's series formula then;

F(0) + f'(0) + f"(0)/2! × x^2 + f'''(0)/3! × x^3.

[ NOTE: f(0) = 3, f''(0) = 30, f'''(0) = 9000, f''''(0) = 225000].

450/2! = 225, 9000/ 3! = 1500 and 225000/4! = 9375..

Which gives; 3 + 30x + 225x^2 + 1500x^3 + 9375x^4. The ratio test will then give us our answer as 1/5.

As stated above, alternatively we can make use of the sum of geometric series where |x| < 1/5

You might be interested in
18 POINTS will rate brainiest 6th grade math
stira [4]

Answer:

18 ft^2

Step-by-step explanation:

The area of a parallelogram is A=bh.

The area would be A = 9*4.

A = 36

To find the area of one trapezoid you divide the area of the parallelogram by 2.

36/2 = 18 ft^2

5 0
3 years ago
Helppp this is killing meee
agasfer [191]

Answer:

(10x+26)=36x

(8x+42)=50x

Step-by-step explanation:

hope this helps!

7 0
3 years ago
Read 2 more answers
Conan installs windows for a living and has propped his ladder against a customer's
Luden [163]

Answer:

Step-by-step explanation:

By the Pythagorean Theorem

h^2=x^2+y^2

Which means that the hypotenuse (longest side of a right triangle) squared is equal to the sum of its squared sides. In this case we are given the side lengths of 8 and 15 feet.

h^2=8^2+15^2

h^2=64+225

h^2=289

h=17 ft

The ladder is 17 feet long.

3 0
2 years ago
-6(2x + 4) = 12 what is the answer <br>​
katrin2010 [14]
The answer to your question is -3 !!
3 0
3 years ago
Read 2 more answers
7/8+ -7/16 ÷ 8/10 -1/4​
larisa [96]

Answer:

5/64

Step-by-step explanation:

used calculator

4 0
2 years ago
Other questions:
  • Please help me please​
    11·1 answer
  • How do you solve x^2+4x-5=0
    14·2 answers
  • Find the Y intercept of a line that passes through 3, -5 and has a slope of -1
    13·1 answer
  • What is the value of x in this figure?
    15·1 answer
  • What is the value of e^ln7 x1<br> 7e<br> 7x<br> 7
    15·1 answer
  • 5. Xian plans to run 14 laps around a track Each lap is 400 yards. So farxian has run 1,680 yards around the track. What percent
    7·1 answer
  • The legs of a right triangle measure 5 inches and 9 inches.
    5·1 answer
  • The account
    13·1 answer
  • a container has 16 1/2 cups of lemonade. Asher gives each of his classmates 3/4 of a cup if lemonade. if asher gives away all of
    10·1 answer
  • Please Solve so i can complete!!!!!!!! Quick Fasts
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!