MATH

posted by .

Expand f(x)=ln (1+x/1-x) in a Taylor Series about x=0. You must express your answer using summation notation.

---This is what I tried to do---
So I was thinking of taking the derivative of ln(1+x/1-x) and get 2/x^2-1

And then use the identity 1/1-x= sum x^k

So then it will be Sum (-2^k) (x^2k)

  • MATH -

    you have the right idea.
    First, df/dx = -2/(1-x^2), but I'd do it like this:

    f(x) = ln(1+x) - ln(1-x)
    ln(1+x) = 0+x-x^2/2+x^3/3-x^4/4+x^5/5+...
    ln(1-x) = 0-x-x^2/2-x^3/3-x^4/4-x^5/5-...
    subtract to get
    0 + 2x + 2x^3/3 + 2x^5/5 + ...

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus-- need help desperately!

    The Taylor series about x=5 for a certain function f converges to f(x) for all x in the interval of convergence. The nth derivative of f at x=5 is given by f^(n) (5)= (-1)^n(n!)/((2^n)(n+2)), and f(5)=1/2. Write third degree Taylor …
  2. Calculus

    Please.... I need your help! I posted this question yesterday and no one has answered it yet. Can anyone help me please?
  3. Calculus - Taylor #2

    Find the Taylor series for f(x) centered at the given value of 'a'. (Assume that 'f' has a power series expansion. Do not show that Rn(x)-->0.) f(x) = x3, a = -1 and what i've done so far: f (x) = x^3 f ' (x) = 3x^2 f '' (x) = 6x^1 …
  4. Algebra

    Express the sum below using summation notation. Use 1 as the lower limits of summation and i for the index of summation. 1/3+2/4+3/5+...+18/20
  5. Calculus

    Hi~ Thank you for your help! I was trying to work on a problem about Taylor series, but i don't think im approaching the problem the right way. I have to find the fifth order Taylor polynomial and Taylor series for the function f(x) …
  6. Calculus Derivative- Taylor Series?

    let f(x)= x/x-1 find f'(x) f ''(x) and a formula for f ^ (n) * x. I found the first and second derivatives but do not know how to make a general equation for this. I have not learnt the Taylor or Maclaurin Series either. Thank you.
  7. Algebra 2

    Use summation notation to write the series 2+4+6+8 for 10 term in each of these images, the lower limit of the summation notation is either n=1, or n=0
  8. Maths

    Use the binomial series to find the Taylor series about 0 for the function f(x) = (1 + x)−3/5, giving all terms up to the one in x4. I have the answer; f(x)=1-3/5(x) +12/25(x^2) -52/125(x^3) + 234/625(x^4) but i am not sure how …
  9. Urgent help Maths Ms sue

    Use binomial series to find the Taylor series about 0 for the function f(x)=(1+x)^-3/5 giving all terms up to the one in x^4. Then use this series and Taylor series for sin x to find the quartic Taylor polynomial about 0 for the function …
  10. Calculus Help Please

    Hello! I am struggling with this problem: Find the Taylor Series for sin(x-2) centered at c=3. My work so far: sin(1)+(x-3)cos(1)-(1/2)(x-3)^2sin(1)-(1/6)(x-3)^3cos(1)+(1/24)(x-3)^4sin(1)... I know that the Taylor series for sign is …

More Similar Questions