Why guess-solution to linear recurrence relation is a exponential?
Sir i am from mechanical engineering. I recently started studying discrete mathematics and algorithms out of self interest.
In solving Fibonacci recurrence relation, $F(n)=F(n-1)+F(n-2)$. we assume $F(n) = x^n$, x is some variable. Why such guessing? I saw this type of function guessing in solving homogeneous linear recurrence relation. May I know is there any specific reason for this? Why not some other function?kindly clarify