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Can someone help me with this binomial expansion? watch

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    (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
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    (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.
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    (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.
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    (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.
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    (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?
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    (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.
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    (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.
 
 
 
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