Question

giải giúp mik nha

          thực  hiện phép tính:

                (1/4.9+1/9.14+1/14.19+...................+1/44.49).1-3-5-7-...............-49/89

                       mik cần gấp ''help me''

Answer 1

\(\frac{1}{4.9}+\frac{1}{9.14}+\frac{1}{14.19}+...+\frac{1}{44.49}=\frac{1}{5}\left(\frac{9-4}{4.9}+\frac{14-9}{9.14}+...+\frac{49-44}{49.44}\right)\)

\(=\frac{1}{5}\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+..+\frac{1}{44}-\frac{1}{49}\right)=\frac{1}{5}\left(\frac{1}{4}-\frac{1}{49}\right)=\frac{9}{196}\)

Xét: \(\frac{1-3-5-7-...-49}{89}=\frac{2-\left(1+3+5+...+49\right)}{89}=\frac{2-\frac{25.50}{2}}{89}=\frac{-623}{89}=-7\)

\(\Rightarrow\left(\frac{1}{4.9}+\frac{1}{9.14}+...+\frac{1}{44.49}\right)\cdot\frac{1-3-5-..-49}{89}=\frac{9}{196}.\left(-7\right)=\frac{-9}{28}\)