Question

tính nhanh 2/3*5+2/5*7+/7*9+....2/13*15

Answer 1

\(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{13\cdot15}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\)

\(=\frac{1}{3}-\frac{1}{15}\)

\(=\frac{4}{15}\)

Answer 2

\(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{13\cdot15}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{13}+\frac{1}{15}-\frac{1}{15}\)

\(=\frac{1}{3}-\frac{1}{15}=\frac{4}{15}\)

Answer 3

\(\frac{2}{3.5}\)+ \(\frac{2}{5.7}\)+ \(\frac{2}{7.9}\)+...+ \(\frac{2}{13.15}\)= \(\frac{1}{3}\)- \(\frac{1}{5}\)+ \(\frac{1}{5}\)- \(\frac{1}{7}\)+ \(\frac{1}{7}\)- \(\frac{1}{9}\)+...+ \(\frac{1}{13}\)- \(\frac{1}{15}\)= \(\frac{1}{3}\)- \(\frac{1}{15}\)= \(\frac{4}{15}\).