Question

Thực hiện phép tính

\(\left(\frac{1}{4.9}+\frac{1}{9.14}+\frac{1}{14.19}+...+\frac{1}{44.49}\right).\frac{1-3-5-7-...-49}{89}\)

Answer 1

\(\left(\frac{1}{4.9}+\frac{1}{9.14}+...+\frac{1}{44.49}\right).\frac{1-3-5-...-49}{89}\)

\(\)\(=\frac{1}{5}.\left(\frac{5}{4.9}+\frac{5}{9.14}+...+\frac{5}{44.49}\right).\frac{1-3-5-...-49}{89}\)

\(=\frac{1}{5}.\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{44}-\frac{1}{49}\right).\frac{\left(1-\frac{24.\left(49+3\right)}{2}\right)}{89}\)

\(=\frac{1}{5}.\left(\frac{1}{4}-\frac{1}{49}\right).\left(-7\right)=-\frac{9}{28}\)