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    Hi for the validity of the binomial expansion, I know it only applies to those with a negative power right ? so in this question I know that the validity only applies to 1/2 x but why isn't -2 shown ? why not -2<mod x<2 ?

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    (Original post by coconut64)
    Hi for the validity of the binomial expansion, I know it only applies to those with a negative power right ?
    For anything other than a positive integer exponent, the binomial expansion forms an infinite series, and as such its validity is restricted to a certain radius of convergence. Your textbook will cover the details.


    so in this question I know that the validity only applies to 1/2 x but why isn't -2 shown ? why not -2<mod x<2 ?

    Thanks
    In your example the series converges if |x/2| < 1

    So, we can say |x|< 2, or -2 < x < 2. Either is valid. If you use the second form, you don't need the modulus signs.
 
 
 
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