Post a New Question


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))
    = (1/2)(1/(1-x/2))
    = (1/2)Σ0∞x/2k

    as you have corrected determined.

  • Calculus -

    Sorry, the last two lines should read:


  • 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

More Related Questions

Post a New Question