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