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Math Help - Can someone explain why (x+y)^(-n) is a infinite rather than finite series?

  1. #1
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    Can someone explain why (x+y)^(-n) is a infinite rather than finite series?

    Hi first post here...,

    So, we have binomial theorem, works great for (x+y)^n with n being a natural number.

    But, what I can't figure out, why does the binomial expansion go on forever if n is negative? Makes no sense to me, should be able to expand it with the same number of terms as when n>0. Is this like a "unsolved" area of math, or is there a reason for the infinite terms?

    Thanks.
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  2. #2
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    Re: Can someone explain why (x+y)^(-n) is a infinite rather than finite series?

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  3. #3
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    Re: Can someone explain why (x+y)^(-n) is a infinite rather than finite series?

    Quote Originally Posted by panthar View Post
    Hi first post here...,

    So, we have binomial theorem, works great for (x+y)^n with n being a natural number.

    But, what I can't figure out, why does the binomial expansion go on forever if n is negative? Makes no sense to me, should be able to expand it with the same number of terms as when n>0. Is this like a "unsolved" area of math, or is there a reason for the infinite terms?

    Thanks.
    The expansion contains terms n and n-1 an n-2 and so on. If n is a positive integer one of these terms will be zero hence wiping out that term and any that come after. If n is fractional or negative none of these terms is ever zero.
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