Bạn tham khảo tại đây nhé: Câu hỏi của Akane Hoshino.

Chúc bạn học tốt!

trời

anh ơi anh anh dẹp cho em nhờ

bạn viết sai đề rồi . phải là 7 . 9 chứ

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 :

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

\(A=\frac{2}{5}\left(\frac{5}{4.9}+\frac{5}{9.14}+\frac{5}{14.19}+...+\frac{5}{504.509}\right)\)

\(A=\frac{2}{5}\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+\frac{1}{14}-\frac{1}{17}+...+\frac{1}{504}-\frac{1}{509}\right)\)

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

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

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

\(A=\frac{1}{7}\left[\frac{1}{2}-\frac{1}{9}+...+\frac{1}{252}-\frac{1}{509}\right]\)

\(A=\frac{1}{7}.\left[\frac{1}{2}-\frac{1}{509}\right]\)

\(A=\frac{1}{7}.\left[\frac{507}{1018}\right]=\frac{507}{7126}\)

mk nghĩ là vậy đó, ủng hộ mk nha

A =\ dfrac {1} {2.9} + \ dfrac {1} {9.7} + \ dfrac {1} {7.19} + ... + \ dfrac {1} {252.509}2 . 91+9 . 71+7 . 1 91+. . .+2 5 2 . 5 0 91

A = 2. (\ dfrac {1} {4.9} + \ dfrac {1} {9.14} + \ dfrac {1} {14.19} + ... + \ dfrac {1} {504.509}4 . 91+9 . 1 41+1 4 . 1 91+. . .+5 0 4 . 5 0 91)

A =\ dfrac {2} {5}52(\ dfrac {1} {4} - \ dfrac {1} {9} + \ dfrac {1} {9} - \ dfrac {1} {14} + \ dfrac {1} {14} - \ dfrac {1} {19} + ... + \ dfrac {1} {504} - \ dfrac {1} {509}41-91+91-1 41+1 41-1 91+. . .+5 0 41-5 0 91)

A =\ dfrac {2} {5}52(\ dfrac {1} {4} - \ dfrac {1} {509}41-5 0 91)

A =\ dfrac {2} {5}52(\ dfrac {509} {2036} - \ dfrac {4} {2036}2 0 3 65 0 9-2 0 3 64)

A =\ dfrac {2} {5}52.\ dfrac {505} {2036}2 0 3 65 0 5

A =\ dfrac {101} {1018}1 0 1 81 0 1

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

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

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

\(B=\frac{1.4+1}{1.4}+\frac{4.7+1}{4.7}+\frac{7.10+1}{7.10}+...+\frac{100.103+1}{100.103}\)

\(B=1+\frac{1}{1.4}+1+\frac{1}{4.7}+...+1+\frac{1}{100.103}\)

\(B=34+\frac{1}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{100.103}\right)\)

\(B=34+\frac{1}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{100}-\frac{1}{103}\right)\)

\(B=34+\frac{1}{3}\left(1-\frac{1}{103}\right)=...\)