posted by Sean on .
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?
1/(1-x) = Î£0âˆžxk
write 1/(2-x) as (1/2)(1/(1-x/2))
as you have corrected determined.
Sorry, the last two lines should read:
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.
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
However, utf-8 may not be available automatically on all computers.
I will take more care with the encoding next time. Thanks.