f(n+2)=2f(n+1)+f(n)

Solution for f(n+2)=2f(n+1)+f(n) equation:

Simplifying
f(n + 2) = 2f(n + 1) + f(n)

Reorder the terms:
f(2 + n) = 2f(n + 1) + f(n)
(2 * f + n * f) = 2f(n + 1) + f(n)
(2f + fn) = 2f(n + 1) + f(n)

Reorder the terms:
2f + fn = 2f(1 + n) + f(n)
2f + fn = (1 * 2f + n * 2f) + f(n)
2f + fn = (2f + 2fn) + f(n)

Multiply f * n
2f + fn = 2f + 2fn + fn

Combine like terms: 2fn + fn = 3fn
2f + fn = 2f + 3fn

Add '-2f' to each side of the equation.
2f + -2f + fn = 2f + -2f + 3fn

Combine like terms: 2f + -2f = 0
0 + fn = 2f + -2f + 3fn
fn = 2f + -2f + 3fn

Combine like terms: 2f + -2f = 0
fn = 0 + 3fn
fn = 3fn

Solving
fn = 3fn

Solving for variable 'f'.

Move all terms containing f to the left, all other terms to the right.

Add '-3fn' to each side of the equation.
fn + -3fn = 3fn + -3fn

Combine like terms: fn + -3fn = -2fn
-2fn = 3fn + -3fn

Combine like terms: 3fn + -3fn = 0
-2fn = 0

Divide each side by '-2'.
fn = 0

Simplifying
fn = 0

The solution to this equation could not be determined.