Finding General Term Of Sequence (unable to understand solved exercise on book)
Given the sequence (An) with An+1 = BAn + C , A1=a, C not zero, B not 1
Find the formula (for general term) of this sequence.
A2 = BA1 + C = BA + C ((1-B)/(1-B))
A3=...=(B^2)a + C((1-B^2)/(1-B))
it continues, then uses math induction etc and gives the solution that An = (B^n-1)M+N
I am not really asking for the result, my problem is very specific, is this:
((1-B)/(1-B))... which I don't understand where came from.
Thank you all!