102學測數學考科-02

<單選>令 \(a = 2.6^{10} – 2.6^9\),\(b = 2.6^{11} – 2.6^{10}\),\(c = \frac{2.6^{11} – 2.6^9}{2}\)。請選出正確的大小關係。
(1) \(a \gt b \gt c\)
(2) \(a \gt c \gt b\)
(3) \(b \gt a \gt c\)
(4) \(b \gt c \gt a\)
(5) \(c \gt b \gt a\)

答案

計算 \(a = 2.6^9 (2.6 - 1) = 2.6^9 \times 1.6\),\(b = 2.6^{10} (2.6 - 1) = 2.6^{10} \times 1.6\),\(c = \frac{2.6^9 (2.6^2 - 1)}{2} = \frac{2.6^9 \times 5.76}{2} = 2.6^9 \times 2.88\)。因此,\(b > c > a\)。正確答案是 (4) \(b > c > a\)。