Calculus

posted by .

Obtain the MacLaurin series for 1/(2-x) by making an appropriate substitution into the MacLaurin series for 1/(1-x).
------------

The MacLaurin series for 1/(1-x) = Σ x^k
I substitue (x-1) in for x, because 1/(2-x) = 1/(1-(x-1))
Making the same substitution in the MacLaurin series gives Σ (x-1)^k

If I manually calculate the MacLaurin series for 1/(2-x), I get Σ x^k/2^(k+1)

Those two don't match. What did I do wrong? Or does that substitution method not work?

  • Calculus -

    1/(1-x) = Σ0∞xk

    write 1/(2-x) as (1/2)(1/(1-x/2))
    then
    1/(2-x)
    = (1/2)(1/(1-x/2))
    = (1/2)Σ0∞x/2k
    =Σ0∞xk+1

    as you have corrected determined.

  • Calculus -

    Sorry, the last two lines should read:

    =(1/2)Σ0∞(x/2)k
    =Σ0∞xk/2k+1

  • Calculus -

    Thanks so much!

    I can't read your symbols, but I can make out what you are doing and it results in the right answer.

  • Calculus -

    Sorry, I was accidentally on unicode.
    You would be able to read the symbols with unicode encoding. If you are on Windows XP, you can use the menu to go
    view/character encoding/utf-8
    However, utf-8 may not be available automatically on all computers.

    I will take more care with the encoding next time. Thanks.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    How do you differentiate the maclaurin series for 1/(1-x) twice to find the maclaurin series of 1/(1-x)^3.
  2. math

    hi if i wanna find the Maclaurin series from another existing series by integrating that series , do i need to include the constant of integration ?
  3. calculus

    Use multiplication of power series to find the first three non-zero terms of the Maclaurin series of e^x ln(1 − x).
  4. calculus

    Use division of power series to find the first three terms of the Maclaurin series for y = sec x.
  5. Calculus

    Find a power series, centered @ x=0, for function f(x)=x/(1+2x). I know this is a maclaurin series, but my work doesn't get the right answer. Can you please show steps?
  6. Calculus

    Find a power series, centered @ x=0, for function f(x)=x/(1+2x). I know this is a maclaurin series, but my work doesn't get the right answer. Can you please show steps?
  7. math

    use sigma notation to write the maclaurin series for the function 1/(1+x)
  8. Calculus II

    So I have Maclaurin series for sinx = ∑(-1)^n[x^(2n+1)]/(2n+1)!. I need to write out new series for sin(x^2). This will be equivalent to squaring the whole Maclaurin series of sinx, right?
  9. Calculus

    The prompt for all of these question is "consider the function f(x) = sin^2(x)". Part A: Write the first four terms of the Maclaurin series for f(x). I assumed this implied non-zero terms, so I found x^2-(1/3)x^4+(2/45)x^6-1/315(x^8). …
  10. Calculus

    Hi, could someone please help me with this question?

More Similar Questions