102學測數學單選第2題詳解

將各數提公因式 $2.6^9$： $$\begin{aligned} a &= 2.6^{10} - 2.6^9 = 2.6^9(2.6 - 1) = 2.6^9 \times 1.6, \\[4pt] b &= 2.6^{11} - 2.6^{10} = 2.6^{10}(2.6 - 1) = 2.6^9 \times 2.6 \times 1.6 = 2.6^9 \times 4.16, \\[4pt] c &= \frac{2.6^{11} - 2.6^9}{2} = \frac{2.6^9(2.6^2 - 1)}{2} = \frac{2.6^9(6.76 - 1)}{2} = 2.6^9 \times 2.88. \end{aligned}$$ 比較倍數大小，因為 $4.16 > 2.88 > 1.6$，所以 $b > c > a$，故選 $(4)$。