Câu hỏi

Tính tích a ) D = 3 2 2 ⋅ 8 3 2 ⋅ 15 4 2 ⋅ 24 5 2 ⋅ 35 6 2 ⋅ 48 7 2 ⋅ 63 8 2 ⋅ 80 9 2 b ) E = 9 8 ⋅ 16 15 ⋅ 25 24 … 2500 2499

Tính tích

$a) D = \frac{2 ^{2}}{3} \cdot \frac{3 ^{2}}{8} \cdot \frac{4 ^{2}}{15} \cdot \frac{5 ^{2}}{24} \cdot \frac{6 ^{2}}{35} \cdot \frac{7 ^{2}}{48} \cdot \frac{8 ^{2}}{63} \cdot \frac{9 ^{2}}{80}$

$b) E = \frac{8}{9} \cdot \frac{15}{16} \cdot \frac{24}{25} \dots \frac{2499}{2500}$

H. Học_Sinh

Giáo viên

Xác nhận câu trả lời

Giải thích

a) D = 1.3 2.2 ⋅ 2.4 3.3 ⋅ 3.5 4.4 … 7.9 8.8 ⋅ 8.10 9.9 = ( 1.2.3 … 7.8 ) ( 3.4.5 … 9.10 ) ( 2.3.4 … 8.9 ) ( 2.3.4 … 8.9 ) = 10 9.2 = 5 9 b) E = 3.3 2.4 ⋅ 4.4 3.5 ⋅ 5.5 4.6 … 50.50 49.51 = ( 3.4.5 … 50 ) ( 3.4.5 … 50 ) ( 2.3.4 … 49 ) ( 4.5.6 … 51 ) = 50.3 2.51 = 25 17

a) $D = \frac{2.2}{1.3} \cdot \frac{3.3}{2.4} \cdot \frac{4.4}{3.5} \dots \frac{8.8}{7.9} \cdot \frac{9.9}{8.10} = \frac{( 2.3.4 \dots 8.9 ) ( 2.3.4 \dots 8.9 )}{( 1.2.3 \dots 7.8 ) ( 3.4.5 \dots 9.10 )} = \frac{9.2}{10} = \frac{9}{5}$

b) $E = \frac{2.4}{3.3} \cdot \frac{3.5}{4.4} \cdot \frac{4.6}{5.5} \dots \frac{49.51}{50.50} = \frac{( 2.3.4 \dots 49 ) ( 4.5.6 \dots 51 )}{( 3.4.5 \dots 50 ) ( 3.4.5 \dots 50 )} = \frac{2.51}{50.3} = \frac{17}{25}$