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Question

Q=(  $1+\frac{1}{1\cdot3}$)  * (  $1+\frac{1}{2\cdot4}$) * (  $1+\frac{1}{3\cdot5}$) * ... * ($1+\frac{1}{99\cdot101}$)

soyeon_Tiểu bàng giải · Accepted Answer

$Q=\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right).\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{99.101}\right)$$Q=\frac{4}{1.3}.\frac{9}{2.4}.\frac{16}{3.5}...\frac{10000}{99.101}$$Q=\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}...\frac{100.100}{99.101}$$Q=\frac{2.3.4...100}{1.2.3...99}.\frac{2.3.4...100}{3.4.5...101}$$Q=100.\frac{2}{101}$$Q=\frac{200}{101}$Câu trả lời: $Q=\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right).\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{99.101}\right)$$Q=\frac{4}{1.3}.\frac{9}{2.4}.\frac{16}{3.5}...\frac{10000}{99.101}$$Q=\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}...\frac{100.100}{99.101}$$Q=\frac{2.3.4...100}{1.2.3...99}.\frac{2.3.4...100}{3.4.5...101}$$Q=100.\frac{2}{101}$$Q=\frac{200}{101}$

Sarah · Answer

$Q=\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right).\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{99.101}\right)$$Q=\frac{4}{1.3}.\frac{9}{2.4}.\frac{16}{3.5}...\frac{10000}{99.101}$$=\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}...\frac{100.100}{99.101}$$Q=\frac{2.3.4...100}{1.2.3...99}.\frac{2.3.4...100}{3.4.5...101}$$Q=100.\frac{2}{101}$$Q=\frac{200}{101}$Câu trả lời: $Q=\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right).\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{99.101}\right)$$Q=\frac{4}{1.3}.\frac{9}{2.4}.\frac{16}{3.5}...\frac{10000}{99.101}$$=\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}...\frac{100.100}{99.101}$$Q=\frac{2.3.4...100}{1.2.3...99}.\frac{2.3.4...100}{3.4.5...101}$$Q=100.\frac{2}{101}$$Q=\frac{200}{101}$

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