RSolve

RSolve[eqn, a[n], n] solves a recurrence equation for a[n].

RSolve[{eqn1, eqn2, ...}, {a1[n], a2[n], ...}, n] solves a system of recurrence equations.

RSolve[eqn, a[n1, n2, ...], {n1, n2, ...}] solves a partial recurrence equation.

Examples

Solve a simple recurrence:

RSolve[a[n] == 2 a[n - 1], a[n], n]
(* {{a[n] -> 2^n C[1]}} *)

Solve with initial condition:

RSolve[{a[n] == a[n - 1] + 1, a[0] == 0}, a[n], n]
(* {{a[n] -> n}} *)

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