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

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

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

Multiply f * n
fn = 2(n + -1) + f(n + -1)

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

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

Reorder the terms:
fn = -2 + -1f + fn + 2n

Add '-1fn' to each side of the equation.
fn + -1fn = -2 + -1f + fn + -1fn + 2n

Combine like terms: fn + -1fn = 0
0 = -2 + -1f + fn + -1fn + 2n

Combine like terms: fn + -1fn = 0
0 = -2 + -1f + 0 + 2n
0 = -2 + -1f + 2n

Solving
0 = -2 + -1f + 2n

Solving for variable 'f'.

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

Add 'f' to each side of the equation.
0 + f = -2 + -1f + f + 2n
Remove the zero:
f = -2 + -1f + f + 2n

Combine like terms: -1f + f = 0
f = -2 + 0 + 2n
f = -2 + 2n

Simplifying
f = -2 + 2n