Question

1. tính nhanh

 A = 2/10,11 + 2/11.12 + 2/12,13 + ................ + 2/ 99,100

MÌNH CẦN NHANH

Answer 1

\(\frac{A}{2}=\frac{1}{10\cdot11}+\frac{1}{11\cdot12}+...+\frac{1}{99\cdot100}\)

\(\frac{A}{2}=\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{99}-\frac{1}{100}\)

\(\frac{A}{2}=\frac{1}{10}-\frac{1}{100}\)

\(\frac{A}{2}=\frac{9}{100}\)

\(A=\frac{9}{50}\)

Answer 2

\(A=\frac{2}{10\cdot11}+\frac{2}{11\cdot12}+\frac{2}{12\cdot13}+...+\frac{2}{99\cdot100}\)

\(A=2\left(\frac{1}{10\cdot11}+\frac{1}{11\cdot12}+\frac{1}{12\cdot13}+...+\frac{1}{99\cdot100}\right)\)

\(A=2\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+...+\frac{1}{99}-\frac{1}{100}\right)\)

\(A=2\left(\frac{1}{10}-\frac{1}{100}\right)\)

\(A=2\cdot\frac{9}{100}\)

\(A=\frac{9}{50}\)