Question

tính nhanh  E= 2/1.4 - 2/4.7 + 2/7.10+...+ 2/31.34

Answer 1

\(E=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{31.34}\)

\(E=\frac{2}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{31.34}\right)\)

\(E=\frac{2}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{31}-\frac{1}{34}\right)\)

\(E=\frac{2}{3}\left(1-\frac{1}{34}\right)\)

\(E=\frac{2}{3}.\frac{33}{34}\)

\(E=\frac{11}{17}\)