Let () be defined recursively as follows: $(1) = $, and $(n) = (/) + $, $\forall \geq 2$
where $, $, and $$ are positive constants, $ \not= 1$, $$ is an arbitrary constant, and $ = $
for some non-negative integer $$. Prove by induction on $k$ that $( ) = [ +/(−1)]^ −/a-1$.
Conclude that $ () = [ +/(−1)]^{\frac{n}{b}} − /−1$.
