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Can someone help me with this binomial expansion?

(1-x/1+x)^1/2

The answer is 1-x+(1/2)x^2

For some reason I am not getting the 1 in this answer I keep getting 2. Thanks
Original post by Reneewinters
(1-x/1+x)^1/2

The answer is 1-x+(1/2)x^2

For some reason I am not getting the 1 in this answer I keep getting 2. Thanks


You've not posted any working, so we can only guess at what you've done.
Original post by ghostwalker
You've not posted any working, so we can only guess at what you've done.


(1-x)^1/2= 1-(1/2)x+(1/8)x^2+........

(1+x)^-1/2= 1-(1/2)x+(3/8)x^2+.........

Then I added the coefficients as you only need the terms up to x^2

I got 2-x+(1/2)x^2

Hope this helps.
Original post by Reneewinters
(1-x)^1/2= 1-(1/2)x+(1/8)x^2+........

(1+x)^-1/2= 1-(1/2)x+(3/8)x^2+.........

Then I added the coefficients as you only need the terms up to x^2

I got 2-x+(1/2)x^2

Hope this helps.


You "added" the ceofff. - therein lies the problem.

The two terms (1-x)^1/2 and (1+x)^-1/2 are multipled together in the given formula. So, you need to multply the two power series together, since each approximates one of the two terms.
(edited 6 years ago)
Original post by ghostwalker
You "added" the ceofff. - therein lies the problem.

The two terms (1-x)^1/2 and (1+x)^-1/2 are multipled together in the given formula. So, you need to multply the two power series together, since each approximates one of the two terms.


Yes I get that but when I multiplied I got terms raised to x^4 and x^3. That I know is incorrect. I obviously acknowledge that there is something wrong with my calculation when I multiplied but the problem is what?

so the terms (1-0.5x+(1/8)x^2) are multiplied with (1-0.5x+(3/8)x^2) correct? But wont x^2 multiplied by x^2 give an answer in x^4?

Can you please solve the question once?
Original post by ghostwalker
You "added" the ceofff. - therein lies the problem.

The two terms (1-x)^1/2 and (1+x)^-1/2 are multipled together in the given formula. So, you need to multply the two power series together, since each approximates one of the two terms.


Actually nevermind, I finally got the answer. Thanks for the help.
Original post by Reneewinters
Yes I get that but when I multiplied I got terms raised to x^4 and x^3. That I know is incorrect.


No, it's not incorrect. Your expansion to x^2 terms is a truncated series - an approximation. When you multiply the two series together, you will get higher terms again, which you're not interested in, so you just truncate the series again to x^2 terms.


so the terms (1-0.5x+(1/8)x^2) are multiplied with (1-0.5x+(3/8)x^2) correct? But wont x^2 multiplied by x^2 give an answer in x^4?


Your first series is incorrect. Should be (1-0.5x-(1/8)x^2)


Edit: I see you've solved it now. I'll leave this in for the benefit of other readers.
(edited 6 years ago)

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