Question

1/2×5-1/3×5+1/3×7+1/4×7+...+1/6×13+1/7×13

Answer 1

Đề phải thế này chứ

\(\frac{1}{2.5}+\frac{1}{3.5}+\frac{1}{3.7}+\frac{1}{4.7}+...+\frac{1}{6.13}+\frac{1}{7.13}\)

=\(\left(\frac{1}{2.5}+\frac{1}{3.5}\right)+\left(\frac{1}{3.7}+\frac{1}{4.7}\right)+...+\left(\frac{1}{6.13}+\frac{1}{7.13}\right)\)

\(=\frac{3+2}{2.3.5}+\frac{3+4}{3.4.7}+...+\frac{6+7}{6.7.13}\)

=\(\frac{5}{2.3.5}+\frac{7}{3.4.7}+..+\frac{13}{6.7.13}\)

=\(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{6.7}\)

=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{6}-\frac{1}{7}\)

=\(\frac{1}{2}-\frac{1}{7}=\frac{5}{14}\)