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\(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+.....+\frac{1}{97.100}=\frac{1}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+....+\frac{3}{97.100}\right)=\frac{1}{3}\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-.......+\frac{1}{97}-\frac{1}{100}\right)=\frac{1}{3}\left(1-\frac{1}{100}\right)=\frac{1}{3}.\frac{99}{100}=\frac{33}{100}\)
Gọi dãy phân số trên là A
A = \(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{97.100}\)
A = \(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{100}\)
A = \(1-\frac{1}{100}\)
A = \(\frac{99}{100}\)
\(A=\frac{1}{1\cdot4}+\frac{1}{4\cdot7}+...+\frac{1}{91\cdot94}=\frac{1}{3}\left(\frac{3}{1\cdot4}+\frac{3}{4\cdot7}+...+\frac{3}{91\cdot94}\right)\)
\(=\frac{1}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{91}-\frac{1}{94}\right)\)
\(=\frac{1}{3}\left[\left(1-\frac{1}{94}\right)+\left(\frac{1}{4}-\frac{1}{4}\right)+...+\left(\frac{1}{91}-\frac{1}{91}\right)\right]\)
\(=\frac{1}{3}\left[\left(\frac{94}{94}-\frac{1}{94}\right)+0+...+0\right]=\frac{1}{3}\cdot\frac{93}{94}=\frac{93}{282}\)
Ta thấy: 1/1-1/4 = 3/4 = 3.(1/1.4)
1/4-1/7 = 3/28 = 3.(1/4.7)
A = 3(1/1-1/4+1/4-1/7+...+1/97-1/100)
A = 3.(1-1/100)
A = 3.(99/100)
A = 297/100
\(A=\frac{1}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+.......+\frac{1}{97}-\frac{1}{100}\right)\)
\(A=\frac{1}{3}.\left(1-\frac{1}{100}\right)\)
\(A=\frac{1}{3}.\frac{99}{100}\)
\(A=\frac{33}{100}\)
Võ Thiện Tuấn viết tổng quát kết quả hay phép đề bài hả bạn ?
\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7} +....+\frac{1}{100}-\frac{1}{103}\)
\(=1-\frac{1}{103}\)
\(=\frac{102}{103}\)
\(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{97.100}\)
\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{97}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
\(\Rightarrow\frac{99}{100}=\frac{0.33.x}{2009}\)
\(\Rightarrow100.0.33.x=99.2009\)
\(\Rightarrow0x=198891\Rightarrow\)không có GT x thỏa mãn
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_
1/1*4+1/4*7+1/7*10+...+1/2010*2013=A
3A=3/1*4+3/4/*7+3/7*10+...+3/2010*2013
3A=1-1/4+1/4-1/7+1/7-1/10+...+1/2010-1/2013
3A=1-1/2013<1
Suy ra : A <1/3
Nho k cho minh voi nhe
\(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{97.100}\)
\(=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+....+\frac{1}{97}-\frac{1}{100}\)
\(=1-\frac{1}{100}=\frac{99}{100}\)
Còn lại thì dễ rồi bạn nhé
cho mk một tk đi bà con ơi
ủng hộ mk đi làm ơn
1/1.4 + 1/4.7 + 1/7.10 + ... + 1/35.38
= 1/3 ( 1/1 - 1/4 + 1/4 - 1/7 + 1/7 - ... - 1/35 + 1/35 - 1/38)
= 1/3 ( 1- 1/38 )
= 1/3 . 37/38
= 37/114
k cho mình nha mí bạn