Question

A=1/1×3 + 2/3×5 + 2/5×7 + ..............2/13×15

Giải rõ cho mình nha

Answer 1

\(A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{13.15}\) (DẤU ''.''LÀ DẤU NHÂN NHA P)

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

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

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

A=\(\frac{14}{15}\)