Question

[Imo Phan]

\(\left(1-\frac{2}{6}\right)\times\left(1-\frac{2}{12}\right)\times\left(1-\frac{2}{20}\right)...\left(1-\frac{2}{9900}\right)\) Tính

Answer 1

[soyeon_Tiểu bàng giải]

(1 - 2/6) × (1 - 2/12) × (1 - 2/20) × ... × (1 - 2/9900)

= 4/6 × 10/12 × 18/20 × ... × 9898/9900

= 1.4/2.3 × 2.5/3.4 × 3.6/4.5 × ... × 98.101/99.100

= 1.2.3...98/3.4.5...100 × 4.5.6...101/2.3.4...99

= 2/99.100 × 100.101/2.3

= 101/99×3 = 101/297

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