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Simplifying f(2n + 1) = f(n + -1) + f(n) + 1 Reorder the terms: f(1 + 2n) = f(n + -1) + f(n) + 1 (1 * f + 2n * f) = f(n + -1) + f(n) + 1 (1f + 2fn) = f(n + -1) + f(n) + 1 Reorder the terms: 1f + 2fn = f(-1 + n) + f(n) + 1 1f + 2fn = (-1 * f + n * f) + f(n) + 1 1f + 2fn = (-1f + fn) + f(n) + 1 Multiply f * n 1f + 2fn = -1f + fn + fn + 1 Reorder the terms: 1f + 2fn = 1 + -1f + fn + fn Combine like terms: fn + fn = 2fn 1f + 2fn = 1 + -1f + 2fn Add '-2fn' to each side of the equation. 1f + 2fn + -2fn = 1 + -1f + 2fn + -2fn Combine like terms: 2fn + -2fn = 0 1f + 0 = 1 + -1f + 2fn + -2fn 1f = 1 + -1f + 2fn + -2fn Combine like terms: 2fn + -2fn = 0 1f = 1 + -1f + 0 1f = 1 + -1f Solving 1f = 1 + -1f 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. 1f + f = 1 + -1f + f Combine like terms: 1f + f = 2f 2f = 1 + -1f + f Combine like terms: -1f + f = 0 2f = 1 + 0 2f = 1 Divide each side by '2'. f = 0.5 Simplifying f = 0.5
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