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Simplifying f(n) = 2(n + -1) + f(n + -2) Multiply f * n fn = 2(n + -1) + f(n + -2) Reorder the terms: fn = 2(-1 + n) + f(n + -2) fn = (-1 * 2 + n * 2) + f(n + -2) fn = (-2 + 2n) + f(n + -2) Reorder the terms: fn = -2 + 2n + f(-2 + n) fn = -2 + 2n + (-2 * f + n * f) fn = -2 + 2n + (-2f + fn) Reorder the terms: fn = -2 + -2f + fn + 2n Add '-1fn' to each side of the equation. fn + -1fn = -2 + -2f + fn + -1fn + 2n Combine like terms: fn + -1fn = 0 0 = -2 + -2f + fn + -1fn + 2n Combine like terms: fn + -1fn = 0 0 = -2 + -2f + 0 + 2n 0 = -2 + -2f + 2n Solving 0 = -2 + -2f + 2n Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '2f' to each side of the equation. 0 + 2f = -2 + -2f + 2f + 2n Remove the zero: 2f = -2 + -2f + 2f + 2n Combine like terms: -2f + 2f = 0 2f = -2 + 0 + 2n 2f = -2 + 2n Divide each side by '2'. f = -1 + n Simplifying f = -1 + n
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