Question

Tính nhanh

E = \(\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)

G = \(\frac{1}{6}+\frac{1}{66}+\frac{1}{176}+...+\frac{1}{336}\)

Answer 1

\(E=\frac{2}{20}+\frac{2}{30}+...+\frac{2}{240}\)

\(\Rightarrow E=\frac{2}{4.5}+\frac{2}{5.6}+...+\frac{2}{15.16}\)

\(E=2.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\right)\)

\(E=2.\frac{3}{16}=\frac{3}{8}\)

 

Answer 2

\(E=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}\)

\(E=\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+...+\frac{2}{15.16}\)

\(E=2.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)\)

\(E=2.\left(\frac{1}{4}-\frac{1}{16}\right)\)

\(E=2.\frac{3}{16}\)

\(E=\frac{3}{8}\)

Answer 3

\(D=\frac{1}{6}+\frac{1}{66}+\frac{1}{176}+...+\frac{1}{336}\)

\(D=\frac{1}{1.6}+\frac{1}{6.11}+\frac{1}{11.16}+...+\frac{1}{16.21}\)

\(D=\frac{1}{5}.\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+...+\frac{1}{16}-\frac{1}{21}\right)\)

\(D=\frac{1}{5}.\left(1-\frac{1}{21}\right)\)

\(D=\frac{1}{5}.\frac{20}{21}\)

\(D=\frac{4}{21}\)