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
e-lub [12.9K]
3 years ago
10

Use the binomial series to expand the function as a power series. (1 − x)^1/5 state radius of convergence.

Mathematics
1 answer:
Lemur [1.5K]3 years ago
7 0

Answer:

Valid only for |x|<1

Step-by-step explanation:

Binomial expansion for rational powers is valid only if

|x|<1

If |x|<1 we have

(1-x)^{\frac{1}{5} } =1+\frac{1}{5} (-x)+\frac{\frac{1}{5} \frac{-4}{5}x^2}{2!} +\frac{\frac{1}{5} \frac{-4}{5} \frac{-9}{5}x^3 }{3!} +...

Same like integral powers except that instead of nCr we write here n(n-1)../r!

and there will be an infinite series

Thus we have

(1-x)^{\frac{1}{5} } =1+\frac{1}{5} (-x)+\frac{\frac{1}{5} \frac{-4}{5}x^2}{2!} +\frac{\frac{1}{5} \frac{-4}{5} \frac{-9}{5}x^3 }{3!} +..\\= 1-\frac{x}{5} -\frac{2x^2}{25} +\frac{12x^3}{125} +...

You might be interested in
Lynn can wash 95 cars in 5 days.<br><br> How many cars can Lynn wash in 11 days?
pav-90 [236]

Answer:

209 cars

Step-by-step explanation:

95/5=19. 19 cars is the unit rate. 19*11=209

3 0
3 years ago
3/4÷5 y multiplica el resultado por 4​
Vlad [161]

Answer:

0.6

Step-by-step explanation:

\frac{3}{4} / 5 = 0.15

0.15 x 4 = 0.6

Hope I helped! Check out my profile for more answers!

¡Espero haber ayudado! ¡Mira mi perfil para obtener más respuestas!

3 0
3 years ago
What is the decimal equivalent of 118 ??
MakcuM [25]
The decimal equivalent of 118 is 118.0 but if you mean what is the decimal equivalent of 118% then the answer is 1.18
7 0
3 years ago
(-12,-1) and (-3,-4)
castortr0y [4]

what do you need to do


7 0
3 years ago
Read 2 more answers
Find the endpoint of the line segment with the given endpoint and midpoint.
dlinn [17]

Answer:

(10, 2)

Step-by-step explanation:

To get from the given endpoint to the midpoint, 6 was added to x and 2 was added to y. As per the definition of a midpoint, the resulting two line segments will be congruent (first endpoint and midpoint congruent to midpoint and second endpoint). Use the same formula (x + 6, y + 2) to find the second endpoint (use the x and y of the midpoint):

(x + 6, y + 2)

(4 + 6, 0 +2)

(10, 2)

8 0
3 years ago
Read 2 more answers
Other questions:
  • there are 7 kids at a birthday party. if there are 4 girls and 3 boys at the party, what fraction of the kids are boys?
    12·2 answers
  • Find the total area of the solid figure with the length, 3 width 5, and height 6
    5·2 answers
  • What is the volume of the prism
    15·2 answers
  • I NEED some help PLEASE!
    8·1 answer
  • Pls help with all of this idk how to do
    6·1 answer
  • Need help with sample mean
    12·1 answer
  • Please help I am stuck. This is due in one hour so please help. ​
    6·2 answers
  • 49 × 66 + 49 × 34 = 49 × ( ____+ _____)​
    14·2 answers
  • Using a loan calculator, find the total cost to repay a two month long short-term loan with a principal of $750 and an interest
    8·2 answers
  • in an election, candidate a got 75% of the total valid votes. if 15% of the total votes were declared invalid and the total numb
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!