Question

Tính

A= \(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{19.21}\)

B= \(\frac{3}{11.14}+\frac{3}{14.17}+\frac{3}{17.20}+...+\frac{3}{68.71}\)

C= \(\frac{8}{9}.\frac{15}{16}.\frac{24}{25}.\frac{35}{36}.............................\frac{2499}{2500}\)

Answer 1

\(A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{19.21}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\)

\(=\frac{1}{3}-\frac{1}{21}\)

\(=\frac{7}{21}-\frac{1}{21}=\frac{6}{21}\)

Answer 2

\(A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{19.21}\)

\(A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\)

\(A=\frac{1}{3}+\left(\frac{1}{5}-\frac{1}{5}\right)+\left(\frac{1}{7}-\frac{1}{7}\right)+\left(\frac{1}{9}-\frac{1}{9}\right)+...+\left(\frac{1}{19}-\frac{1}{19}\right)-\frac{1}{21}\)

\(A=\frac{1}{3}-\frac{1}{21}\)

\(A=\frac{2}{7}\)

Answer 3

\(B=\frac{3}{11.14}+\frac{3}{14.17}+\frac{3}{17.20}+...+\frac{3}{68.71}\)

\(=\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{21}+...+\frac{1}{68}-\frac{1}{71}\)

\(=\frac{1}{11}-\frac{1}{71}\)

\(=\frac{71}{781}-\frac{11}{781}\)

\(=\frac{60}{781}\)

Answer 4

\(B=\frac{3}{11.14}+\frac{3}{14.17}+\frac{3}{17.20}+...+\frac{3}{68.71}\)

\(B=\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+\frac{1}{17}-\frac{1}{20}+...+\frac{1}{68}-\frac{1}{71}\)

\(B=\frac{1}{11}+\left(\frac{1}{14}-\frac{1}{14}\right)+\left(\frac{1}{17}-\frac{1}{17}\right)+\left(\frac{1}{20}-\frac{1}{20}\right)+...+\left(\frac{1}{68}-\frac{1}{68}\right)-\frac{1}{71}\)

\(B=\frac{1}{11}-\frac{1}{71}\)

\(B=\frac{60}{781}\)

Answer 5

\(C=\frac{8}{9}.\frac{15}{16}.\frac{24}{25}.\frac{35}{36}.........\frac{2499}{2500}\)

\(C=\frac{2.4}{3.3}.\frac{3.5}{4.4}.\frac{4.6}{5.5}...........\frac{49.50}{50.50}\)

\(C=\frac{2.4.3.5.4.6.......49.51}{3.3.4.4.5.5.......50.50}\)

\(C=\frac{2.51}{3.50}\)

\(C=\frac{17}{25}\)

Answer 6

\(A=\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{19.21}\)

\(\Rightarrow A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}\)

\(\Rightarrow A=\frac{1}{3}-\frac{1}{21}\)

\(\Rightarrow A=\frac{2}{7}\)

Answer 7

\(A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{19.21}\)

   \(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\)

    \(=\frac{1}{3}-\frac{1}{21}\)

    \(=\frac{6}{21}\)

    \(=\frac{2}{7}\)

Study well ! >_<

Answer 8

\(B=\frac{3}{11.14}+\frac{3}{14.17}+...+\frac{3}{68.71}\)

\(\Rightarrow B=\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+...+\frac{1}{68}-\frac{1}{71}\)

\(\Rightarrow B=\frac{1}{11}-\frac{1}{71}\)

\(\Rightarrow B=\frac{60}{781}\)