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# Validity in binomial expansion watch

1. 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 ?

Thanks
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2. (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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