Question

[Cô Bé Bí Ẩn]

B = 3/4 * 8/9 * 15 / 16 * ... * 9999/ 10000

C = ( 1 + 1/2 )* (1+1/3 ) * ( 1+1/4 ) * .....* ( 1+ 1/99) * ( 1+1/100)

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Answer 1

[๛Ňɠũ Vị Čáէツ]

\(B=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}...\frac{9999}{10000}\)

\(B=\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}...\frac{9999}{100^2}\)

\(B=\frac{3.8.15...9999}{2^2.3^2.4^2...100^2}\)

\(B=\frac{1.3.2.4.3.5...99.101}{2.2.3.3.4.4...100.100}\)

\(B=\frac{\left(1.2.3...99\right).\left(3.4.5...101\right)}{\left(2.3.4...100\right).\left(2.3.4...100\right)}\)

\(B=\frac{1.101}{100.2}\)

\(B=\frac{101}{200}\)

          \(C=\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).\left(1+\frac{1}{4}\right)...\left(1+\frac{1}{99}\right).\left(1+\frac{1}{100}\right)\)

           \(C=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}...\frac{100}{99}.\frac{101}{100}\)

            \(C=\frac{3.4.5...100.101}{2.3.4...99.100}\)

           \(C=\frac{101}{2}\)

 Dấu . là dâú x nha