\(A=\frac{1}{2.9}+\frac{1}{9.7}+...+\frac{1}{252.509}\)

\(A=\frac{2}{4.9}+\frac{2}{9.14}+...+\frac{2}{504.509}\)

\(A=\frac{2}{5}.\left(\frac{5}{4.9}+\frac{5}{9.14}+...+\frac{5}{504.509}\right)\)

\(A=\frac{2}{5}.\left(\frac{9-4}{4.9}+\frac{14.9}{9.14}+...+\frac{509-504}{504.509}\right)\)

\(A=\frac{2}{5}.\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{504}-\frac{1}{509}\right)\)

\(A=\frac{2}{5}.\left(\frac{1}{4}-\frac{1}{509}\right)\)

\(A=\frac{2}{5}.\frac{505}{2036}\)

\(A=\frac{101}{1018}\)

\(B=\frac{1}{10.9}+\frac{1}{18.13}+\frac{1}{26.17}+...+\frac{1}{802.405}\)

\(\frac{1}{2}B=\frac{1}{10.9.2}+\frac{1}{18.13}+\frac{1}{26.17}+...+\frac{1}{802.405.2}\)

\(\frac{1}{2}B=\frac{1}{10.18}+\frac{1}{18.26}+\frac{1}{26.34}+...+\frac{1}{802.810}\)

\(4B=\frac{8}{10.18}+\frac{8}{18.26}+\frac{8}{26.34}+...+\frac{8}{802.810}\)

\(4B=\frac{18-10}{10.18}+\frac{26-18}{28.26}+\frac{34-26}{26.34}+...+\frac{810-802}{802.810}\)

\(4B=\frac{1}{10}-\frac{1}{18}+\frac{1}{18}-\frac{1}{26}+\frac{1}{26}-\frac{1}{34}+...+\frac{1}{802}-\frac{1}{810}\)

\(4B=\frac{1}{10}-\frac{1}{810}\)

\(4B=\frac{8}{81}\)

\(B=\frac{2}{81}\)

\(C=\frac{2}{4.7}-\frac{3}{5.9}+\frac{2}{7.10}-\frac{3}{9.13}+...+\frac{2}{301.304}-\frac{3}{401.405}\)

\(C=\left(\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{301.304}\right)-\left(\frac{3}{5.9}+\frac{3}{9.13}+...+\frac{3}{401.405}\right)\)

\(C=\frac{2}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{301}-\frac{1}{304}\right)-\frac{3}{4}.\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{401}-\frac{1}{405}\right)\)

\(C=\frac{2}{3}.\left(\frac{1}{4}-\frac{1}{304}\right)-\frac{3}{4}.\left(\frac{1}{5}-\frac{1}{405}\right)\)

\(C=\frac{2}{3}.\frac{75}{304}-\frac{3}{4}.\frac{16}{81}\)

\(C=\frac{25}{152}-\frac{4}{27}\)

\(C=\frac{67}{4104}\)

7A=1/2-1/509=507/1018

a)b) Bạn nhân cả tử và mẫu với 2. Mình làm luôn, ko ghi lại đề bài

a)\(\frac{2}{4.9}+\frac{2}{9.14}+\frac{2}{14.19}+...+\frac{2}{504.509}\)

=\(\frac{2}{5}.\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+\frac{1}{14}-\frac{1}{19}+...+\frac{1}{504}-\frac{1}{509}\right)\)

=\(\frac{2}{5}.\left(\frac{1}{4}-\frac{1}{509}\right)\)

=\(\frac{2}{5}.\frac{505}{2036}=\frac{101}{1018}\)

b)\(\frac{2}{10.18}+\frac{2}{18.26}+\frac{2}{26.34}+...+\frac{2}{802.810}\)

=\(\frac{1}{4}\left(\frac{1}{10}-\frac{1}{18}+\frac{1}{18}-\frac{1}{26}+\frac{1}{26}-\frac{1}{34}+...+\frac{1}{802}-\frac{1}{810}\right)\)

=\(\frac{1}{4}.\left(\frac{1}{10}-\frac{1}{810}\right)\)

=\(\frac{1}{4}.\frac{8}{81}=\frac{2}{81}\)

c) Mình biết làm, ddoiwtj tí nữa mình làm cho. Giờ đang mỏi tay

Thẳng Nobita kun có chép bài thì đừng t..i..c..k cho nó

Đề bài của bạn thật là khó hiểu 

cũng khó đó

A=\(\frac{1}{2.9}+\frac{1}{9.7}+\frac{1}{7.19}+...+\frac{1}{252.509}\)

 =\(\frac{1}{2}-\frac{1}{509}\)

 =\(\frac{507}{1018}\)

b)\(\dfrac{1}{7}B=\dfrac{1}{10.18}+\dfrac{1}{18.26}+\dfrac{1}{26.34}+...+\dfrac{1}{802.810}\)

\(\dfrac{1}{7}B=\dfrac{1}{8}\left(\dfrac{8}{10.18}+\dfrac{8}{18.26}+\dfrac{8}{26.34}+...+\dfrac{8}{802.810}\right)\)

\(\dfrac{1}{7}B=\dfrac{1}{8}\left(\dfrac{1}{10}-\dfrac{1}{18}+\dfrac{1}{18}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{34}+...+\dfrac{1}{802}-\dfrac{1}{810}\right)\)

\(\dfrac{1}{7}B=\dfrac{1}{8}\left(\dfrac{1}{10}-\dfrac{1}{810}\right)\)

\(\dfrac{1}{7}B=\dfrac{1}{8}.\dfrac{8}{81}\)

\(\dfrac{1}{7}B=\dfrac{1.8}{8.81}\)

\(\dfrac{1}{7}B=\dfrac{1}{81}\)

\(B=\dfrac{1}{81}:\dfrac{1}{7}\)

\(B=\dfrac{7}{81}\)