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

• May 6th 2012, 10:41 PM
panthar
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.
• May 6th 2012, 11:02 PM
princeps
Re: Can someone explain why (x+y)^(-n) is a infinite rather than finite series?
• May 6th 2012, 11:10 PM
biffboy
Re: Can someone explain why (x+y)^(-n) is a infinite rather than finite series?
Quote:

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.