Question

 Bài 7 : 

Answer 1

Bài 6:

\(B=\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\cdots+\frac{1}{37\cdot38\cdot39}\)

\(=\frac12\left(\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+\cdots+\frac{2}{37\cdot38\cdot39}\right)\)

\(=\frac12\left(\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+\cdots+\frac{1}{37\cdot38}-\frac{1}{38\cdot39}\right)\)

\(=\frac12\left(\frac12-\frac{1}{38\cdot39}\right)=\frac12\cdot\frac{19\cdot39-1}{38\cdot39}=\frac{740}{2964}=\frac{370}{1482}=\frac{185}{741}\)

Bài 7:

a: \(A=\frac{2^2}{1\cdot3}\cdot\frac{3^2}{2\cdot4}\cdot\ldots\cdot\frac{20^2}{19\cdot21}\)

\(=\frac{2\cdot3\cdot\ldots\cdot20}{1\cdot2\cdot\ldots\cdot19}\cdot\frac{2\cdot3\cdot\ldots\cdot20}{3\cdot4\cdot\ldots\cdot21}=\frac{20}{1}\cdot\frac{2}{21}=\frac{40}{21}\)

b: \(B=\frac{1^2}{1\cdot2}\cdot\frac{2^2}{2\cdot3}\cdot\ldots\cdot\frac{10^2}{10\cdot11}\)

\(=\frac12\cdot\frac23\cdot\ldots\cdot\frac{10}{11}=\frac{1}{11}\)