Thread: 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.

link

Originally Posted by panthar

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.