DiscreteRatio

DiscreteRatio[f, i] gives the discrete ratio f(i+1)/f(i).

DiscreteRatio[f, {i, n}] gives the multiple discrete ratio.

DiscreteRatio[f, {i, n, h}] gives the multiple discrete ratio with step h.

Examples

Basic ratio:

DiscreteRatio[f[i], i]
(* f[1 + i]/f[i] *)

Factorial ratio:

DiscreteRatio[i!, i]
(* 1 + i *)

Please visit the official Wolfram Language Reference for more details.