Expert: Ahmed Salami - 12/2/2005

Question
How would you write a power series for a double alternating sign without spliting the series up?

i.e. 1+1-1-1+1+1-1-1

I know if it was 1-1+1-1+1 the answer would be
 (-1)^k  

Answer
Hi Matt,
I'm sorry for the time taken, i was away for the weekend.
Well, it looks like you could put it as
(-1)^(k/2 - 1) for k even
(-1)^(k-1)/2 for k odd
But if you call that splitting, try the recurrence relationship
T(k) = (-1)^k . T(k-1)
Please let me know what you make of it by getting back to me. Forgive the delay.
Regards.