@vv 

Is it possible to use sumrecursion command of the sumtools package to get a simple recurrence relation satisfied by A(i) and then show that A(i)=(-d)^i

@Axel Vogt

I have rewritten the question in maple syntax  

Many thanks

@Kitonum 

Thanks a lot 

This works very well 

@nm  Thank you very much 

@vv  Yes  I obtained this expression

Thank you very much  

@acer Thanks a lot 

I am very grateful