Rút gọn C = (1 + 3^4 + 3^8 + 3^12) / (1 + 3^2 + 3^4 + 3^6+ 3^4 + x^8 + 3^10
Rút gọn C = \(\frac{{1 + {3^4} + {3^8} + {3^{12}}}}{{1 + {3^2} + {3^4} + {3^6} + {3^4} + {3^8} + {3^{10}} + {3^{12}} + {3^{14}}}}\).
Rút gọn C = \(\frac{{1 + {3^4} + {3^8} + {3^{12}}}}{{1 + {3^2} + {3^4} + {3^6} + {3^4} + {3^8} + {3^{10}} + {3^{12}} + {3^{14}}}}\).
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.