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tui chỉ làm phần b thôi há !
B=\(\frac{3}{4}\)+\(\frac{27}{28}\)+\(\frac{69}{70}\)+...+\(\frac{867}{868}\)=\(\frac{4-1}{4}\)+\(\frac{28-1}{28}\)+\(\frac{70-1}{70}\)+...+\(\frac{868-1}{868}\)
= 1+1+..+1 -(\(\frac{1}{4}\)+\(\frac{1}{28}\)+\(\frac{1}{70}\)+...+\(\frac{1}{868}\)) = 10 - \(\frac{1}{3}\)(\(\frac{3}{1.4}\)+\(\frac{3}{4.7}\)+\(\frac{3}{7.10}\)+...+\(\frac{3}{28.31}\))
=10-\(\frac{1}{3}\)(1-\(\frac{1}{4}\)+\(\frac{1}{4}\)-\(\frac{1}{7}\)+\(\frac{1}{7}\)-\(\frac{1}{10}\)+...+\(\frac{1}{28}\)-\(\frac{1}{30}\))=10-\(\frac{1}{3}\)(1-\(\frac{1}{30}\))=10-\(\frac{1}{3}\).\(\frac{29}{30}\)=10-\(\frac{29}{30}\)=\(\frac{271}{30}\)
=\(\frac{1}{3}\times\left(\frac{2}{1}-\frac{2}{4}+\frac{2}{4}-\frac{2}{8}+...+\frac{2}{28}-\frac{2}{31}\right)\)
=\(\frac{1}{3}\times\left(\frac{2}{1}-\frac{2}{31}\right)=\frac{20}{31}\)
Bấm đúng cho tui, đi mà. CHÚC BẠN HỌC GIỎI
bài giải đó là sai giả như vầy nè
\(=\frac{1}{3}\cdot2\cdot\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{8}+...+\frac{1}{28}-\frac{1}{31}\right)\)
\(=\frac{2}{3}\left(1-\frac{1}{31}\right)\)
=\(\frac{2}{3}\cdot\frac{30}{31}=\frac{20}{31}\)
\(A=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+.....+\frac{1}{97}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
Trả lời
\(A=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{4.7}+...+\frac{3}{97.100}\)
\(A=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{97}-\frac{1}{100}\)
\(A=1-\frac{1}{100}\)
\(A=\frac{99}{100}\)
\(B=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+..+\frac{3}{97.100}\)
\(=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-....+\frac{1}{94}-\frac{1}{97}+\frac{1}{97}-\frac{1}{100}\)
\(=\frac{1}{1}-\frac{1}{100}\)
\(=\frac{100}{100}-\frac{1}{100}\)
\(=\frac{99}{100}\)
\(\frac{5}{1.4}+\frac{5}{4.7}+\frac{5}{7.10}+...+\frac{5}{100.103}\)
\(=\frac{5}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{100}-\frac{1}{103}\right)\)
\(=\frac{5}{3}\left(1-\frac{1}{103}\right)\)
\(=\frac{5}{3}.\frac{102}{103}=\frac{170}{103}\)
\(\frac{5}{1.4}+\frac{5}{4.7}+\frac{5}{7.10}+...+\frac{5}{100.103}=\frac{5}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{100.103}\right)=\frac{5}{3}.\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{100}-\frac{1}{103}\right)=\frac{5}{3}.\left(\frac{1}{1}-\frac{1}{103}\right)=\frac{5}{3}.\frac{102}{103}=\frac{170}{103}\)
Ta có : 1/ 1.4 + 1/ 4.7 + .... + 1/ 2016.2019 .
= 1 - 1/4 + 1/4 - 1/7 + ... + 1/2016 - 1/2019 .
= 1 - 1/2019 .
= 2018/2019 .
\(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{2016.2019}\)
\(=\frac{1}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{2016.2019}\right)\)
\(=\frac{1}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{2016}-\frac{1}{2019}\right)\)
\(=\frac{1}{3}.\left(1-\frac{1}{2019}\right)\)
\(=\frac{1}{3}.\frac{2018}{2019}\)
\(=\frac{2018}{6057}\)
_Chúc bạn học tốt_
= 3(1/1.4+1/4.7+1/7.10+.......+1/40.43)
=3(1-1/4+1/4-1/7+1/7-1/10+....+1/40-1/43)
=3(1-1/43)
=3.42/43
=126/43