- #1

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I'm having a good deal of difficulty understanding why the following expansion has an infinite number of terms within it:

(1+x)

^{n}(|x|<1 where n is any real number)

Would someone mind explaining this to me please?

Thanks,

Oscar

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- Thread starter 2^Oscar
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- #1

- 45

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I'm having a good deal of difficulty understanding why the following expansion has an infinite number of terms within it:

(1+x)

Would someone mind explaining this to me please?

Thanks,

Oscar

- #2

- 263

- 1

I'm having a good deal of difficulty understanding why the following expansion has an infinite number of terms within it:

(1+x)^{n}(|x|<1 where n is any real number)

Would someone mind explaining this to me please?

Thanks,

Oscar

If n was an integer there would be n terms, but how do you suppose someone expands [tex](1+x)^\sqrt{2}[/tex]?

- #3

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I think he is referring to Newton's form of the binominal theorem for the absolute value of n less than 1.

Something like[tex] \sqrt{x+1}= x+\frac{1}{2x}-\frac{1}{8x^3}+-[/tex] In the case of x=5^2, we can expand like

[tex]\sqrt{5^2+1} = 5+1/10-1/1000+-+ =5 +99/1000 =5.099 +-+[/tex] This is sometimes a convient way to get rough answers mentally.

Something like[tex] \sqrt{x+1}= x+\frac{1}{2x}-\frac{1}{8x^3}+-[/tex] In the case of x=5^2, we can expand like

[tex]\sqrt{5^2+1} = 5+1/10-1/1000+-+ =5 +99/1000 =5.099 +-+[/tex] This is sometimes a convient way to get rough answers mentally.

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CRGreathouse

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