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Ta có:\(\frac{1}{2.9}=\frac{1}{2}-\frac{1}{9}\)
\(\frac{1}{9.7}=\frac{1}{9}-\frac{1}{7}\)
\(⋮\)
\(\frac{1}{252.504}=\frac{1}{252}-\frac{1}{504}\)
\(A=\frac{1}{2}-\frac{1}{9}+\frac{1}{9}-\frac{1}{7}+\frac{1}{7}-...............+\frac{1}{252}-\frac{1}{504}\)
\(A=\frac{1}{2}-\frac{1}{504}\)
\(A=\frac{251}{504}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt \(A=\frac{1}{2.9}+\frac{1}{9.7}+\frac{1}{7.19}+...+\frac{1}{252.509}\)
\(\Leftrightarrow A=\frac{2}{5}.\left(\frac{5}{4.9}+\frac{5}{9.14}+\frac{5}{14.19}+...+\frac{5}{504.509}\right)\)
\(\Leftrightarrow A=\frac{2}{5}.\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+\frac{1}{14}-\frac{1}{19}+...+\frac{1}{504}-\frac{1}{509}\right)\)
\(\Leftrightarrow A=\frac{2}{5}.\left(\frac{1}{4}-\frac{1}{509}\right)\)
\(\Leftrightarrow A=\frac{2}{5}.\frac{505}{2036}\)
\(\Leftrightarrow A=\frac{101}{1018}\)
~ Hok tốt ~
#)Giải :
\(A=\frac{1}{2.9}+\frac{1}{9.7}+\frac{1}{7.19}+...+\frac{1}{252.509}\)
\(A=\frac{2}{5}\left(\frac{5}{4.9}+\frac{5}{9.14}+\frac{5}{14.19}+...+\frac{5}{504.509}\right)\)
\(A=\frac{2}{5}\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+...+\frac{1}{504}-\frac{1}{509}\right)\)
\(A=\frac{2}{5}\left(\frac{1}{4}-\frac{1}{509}\right)\)
\(A=\frac{2}{5}\times\frac{505}{2036}\)
\(A=\frac{101}{1018}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
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
![](https://rs.olm.vn/images/avt/0.png?1311)
A=\(\frac{1}{2.9}+\frac{1}{9.7}+\frac{1}{7.19}+...+\frac{1}{252.509}\)
=\(\frac{1}{2}-\frac{1}{509}\)
=\(\frac{507}{1018}\)
\(\frac{101}{1018}\)