The solution of the difference equation with the 'initial condition' is...
(1)
... so that is...
(2)
Now we consider separately the terms of (2)...
(3)
(4)
... so that the series (2) converges for and is...
(5)
Kind regards
Thanks so much for your reply chisigma!
How did you get equation 1 though?
I have been looking for tutorials online for "difference equation" and not making much sense of it.
For eg. If its a similar question with a different sequence
How would you equate the "difference equation"
Thanks again
A great 'Thank You' to Plato for having found my mistake... a mistake caused by my superficiality ...
If we have a linear first order difference equation of the form...
, (1)
... its solution is...
(2)
... where . In this case the difference equation is...
, (3)
... so that is , and and the solution of (3) is...
(4)
The first term was correct and the same is for its contribution to ... the contribution of the second term has to be evaluated...
Kind regards