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    Cheeky little question in a textbook seems to be a style of questions i simply can't comprehend,

    obtain the first 4 terms of the expansion:

    ( 1 + (x/100) )^1/2

    hence estimate the value of (102)^1/2

    I have got the terms correctly but can't get the estimate. I tried putting x = 10100 which gives 1 + 101 but that conflicts with the validity of the expansion (-100 < x < 100).

    Please help meh.
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    (Original post by B.Carmine)
    Cheeky little question in a textbook seems to be a style of questions i simply can't comprehend,

    obtain the first 4 terms of the expansion:

    ( 1 + (x/100) )^1/2

    hence estimate the value of (102)^1/2

    I have got the terms correctly but can't get the estimate. I tried putting x = 10100 which gives 1 + 101 but that conflicts with the validity of the expansion (-100 < x < 100).

    Please help meh.
    Hint 1: if x = 2, then it's not far off what you want right? Think about it.
    Hint 2:
    Spoiler:
    Show
    It's off by a certain factor no?
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    (Original post by B.Carmine)
    Cheeky little question in a textbook seems to be a style of questions i simply can't comprehend,

    obtain the first 4 terms of the expansion:

    ( 1 + (x/100) )^1/2

    hence estimate the value of (102)^1/2

    I have got the terms correctly but can't get the estimate. I tried putting x = 10100 which gives 1 + 101 but that conflicts with the validity of the expansion (-100 < x < 100).

    Please help meh.
    Sub x=2 to get \left(1 + \frac{2}{100}\right)^{1/2} = \left(\frac{102}{100}\right)^{1/2} = \frac{\sqrt{102}}{10} \approx \text{expansion}
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    Ah ok, so these questions are a matter of playing with the expression. Ok, thankyou both!
 
 
 
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