Rút gọn C = (1 + 3^4 + 3^8 + 3^12) / (1 + 3^2 + 3^4 + 3^6+ 3^4 + x^8 + 3^10

Đặt A = \(1 + {3^4} + {3^8} + {3^{12}}\)

3⁴ . A = 3⁴ + 3⁸ + 3¹² + 3¹⁶

80A = 3¹⁶ – 1

A = \(\frac{{{3^{16}} - 1}}{{80}}\)

Đặt B = \(1 + {3^2} + {3^4} + {3^6} + {3^4} + {3^8} + {3^{10}} + {3^{12}} + {3^{14}}\)

3² . B = 3² + 3⁴ + 3⁶ + 3⁸ + 3¹⁰ + 3¹² + 3¹⁴ + 3¹⁶

8B = 3² + 3⁴ + 3⁶ + 3⁸ + 3¹⁰ + 3¹² + 3¹⁴ + 3¹⁶ – 1 = 3¹⁶ – 1

B = \(\frac{{{3^{16}} - 1}}{8}\)

Vậy C = \(\frac{A}{B}\)= \(\frac{{{3^{16}} - 1}}{{80}}\):\(\frac{{{3^{16}} - 1}}{8}\) = 0,1.