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
Gala2k [10]
3 years ago
8

Find a power series representation for the function. (Give your power series representation centered at x=0 .) f(x)=15+x

Mathematics
1 answer:
Anna71 [15]3 years ago
4 0

Answer:

f(x) = \sum\limits^{\infty}_{n=0} \frac{-(1)^n\cdot x^n}{5^{n+1}}

Step-by-step explanation:

Given

f(x) = \frac{1}{5 + x}

Required

The power series centered at x = 0

We have:

f(x) = \frac{1}{5 + x}

Factor out 5 from the denominator

f(x) = \frac{1}{5(1 + \frac{x}{5})}

Rewrite as:

f(x) = \frac{\frac{1}{5}}{(1 + \frac{x}{5})}

Further, rewrite as:

f(x) = \frac{1}{5}(1 + \frac{x}{5})^{-1}

Expand the bracket

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

Evaluate all exponents

f(x) = \frac{1}{5}(1 - \frac{x}{5} + \frac{x^2}{25} - \frac{x^3}{125}+......)

Open brackets

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

Notice the pattern as:

f(x) = \frac{1}{5} - \frac{x}{5^2} + \frac{x^2}{5^3} - \frac{x^3}{5^4}+......\± \frac{x^n}{5^{n+1}}

So, the power series is:

f(x) = \sum\limits^{\infty}_{n=0} \frac{-(1)^n\cdot x^n}{5^{n+1}}

You might be interested in
1 divided by root6 - root11 + root5. urgent
vodomira [7]
1/√6      -  √11        + √5

LCM = √6

(1 - (√6)*(√11) + (√5)*(√6) ) / √6


(1 - √(6*11)   + √(5*6) )/ √6


Rationalize the surd by multiplying top and bottom by  √6

((1 - √(6*11)   + √(5*6) )/ √6)    * (√6/√6)


(√6 -  √(6*6*11) + √(5*6*6)) /  √6

(√6 -  6√(11) + 6√(5)) /  6

So answer is:

(√6 -  6√11 + 6√5) / 6
3 0
4 years ago
I like to think of myself as the most lucky person out there. 'Why?' you may ask. My reasoning is quite simple, really. The reas
dusya [7]
That’s really nice man. I’m sure she’ll love it
5 0
3 years ago
Refer to the information in number 1 above to answer this question and exercise #6 below. Write an equation expressing your mont
joja [24]
Any pictures t go along with this so that it will help me give you a better answer?
3 0
4 years ago
Nancy borrows $5000 at a rate of 16% interest per year. What is the amount due at the of 5 hears if the interest is compunded co
Julli [10]
The amount due in 5 years is 11,000
4 0
4 years ago
Read 2 more answers
M is directly proportional to r^2. When r=2 m=14. Work out the value of m when r=12
7nadin3 [17]

Answer:

PLEASE HELLP ME FOR MATHS

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • A baker is making cakes.
    9·2 answers
  • 5 5/3 as a simplified radical expression
    12·1 answer
  • Write the polynomial in standard form. then name the polynomial based on its degree and number of terms.
    14·1 answer
  • Two less than 3/2 of a number (x) is more than 5 1/2
    11·1 answer
  • Please help me with this √(x²-36)=8​
    8·2 answers
  • 2+2= whattttt someone help
    11·2 answers
  • At the beginning of the year office supplies of $1200 for on hand. During the year, boat air conditioning service paid $6000 for
    11·1 answer
  • Evaluate if x=5 xsquard+10=
    15·1 answer
  • The best fitting line minimizes the sum of the squared errors when using ______. Multiple choice question. the high-low method s
    8·1 answer
  • On a coordinate plane, a curved line with a minimum value of (negative 2.5, negative 12) and a maximum value of (0, negative 3)
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!