Nth term of alternating series with two positive terms at beginning

[greg9381]

(I hope this is the right subforum)
I'm talking about the series 1, 1, -1, 1, -1, 1, -1... I thought about it for a long time but I have no idea. If that first term were gone it would just be (-1)^(n+1), but...it's there...

 

[Mark44]

(I hope this is the right subforum)
I'm talking about the series 1, 1, -1, 1, -1, 1, -1... I thought about it for a long time but I have no idea. If that first term were gone it would just be (-1)^(n+1), but...it's there...

Just write it as 1 + your alternating series.

 

[pwsnafu]

(I hope this is the right subforum)
I'm talking about the series 1, 1, -1, 1, -1, 1, -1... I thought about it for a long time but I have no idea. If that first term were gone it would just be (-1)^(n+1), but...it's there...

What's wrong with a₁ = 1, and a_n = (-1)ⁿ for n > 1?

 

[greg9381]

Yeah that works, I was just wondering if there was a better way to do it.