Tính tổng:
\(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{97.100}\)
Tính nhanh
\(A=\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+...+\frac{1}{97.100}\)
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
\(A=\frac{1}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+.......+\frac{1}{97}-\frac{1}{100}\right)\)
\(A=\frac{1}{3}.\left(1-\frac{1}{100}\right)\)
\(A=\frac{1}{3}.\frac{99}{100}\)
\(A=\frac{33}{100}\)
(\(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+..........+\frac{1}{97.100}=\frac{0.33.x}{2009}\))
\(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{97.100}\)
\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{97}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
\(\Rightarrow\frac{99}{100}=\frac{0.33.x}{2009}\)
\(\Rightarrow100.0.33.x=99.2009\)
\(\Rightarrow0x=198891\Rightarrow\)không có GT x thỏa mãn
\(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+........+\frac{1}{97.100}=\frac{0.33..x}{2009}\)
giúp mik nhé
mk đc thầy cho làm bài này rồi nên cảm thấy nó dễ mà
\(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{97.100}\)
\(=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+....+\frac{1}{97}-\frac{1}{100}\)
\(=1-\frac{1}{100}=\frac{99}{100}\)
Còn lại thì dễ rồi bạn nhé
\(S=\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{97.100}\)
=> S = \(\frac{1}{3}\left(\frac{1}{1.4}+\frac{1}{4.7}+....+\frac{1}{97.100}\right)\)
= \(\frac{1}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+....+\frac{1}{97}-\frac{1}{100}\right)\)
= \(\frac{1}{3}\left(1-\frac{1}{100}\right)=\frac{1}{3}.\frac{99}{100}=\frac{33}{100}\)
\(S=\frac{1}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{100}\right)\)
\(S=\frac{1}{3}\left(1-\frac{1}{100}\right)\)
\(S=\frac{1}{3}.\frac{99}{100}=\frac{33}{100}\)
1-1/4cong 1/4 -1/7 cong.....cong 1/97-1/100
1-1/100
99/100
tính tổng
A=\(\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{97.100}\)
\(A=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{97.100}\)
\(A=\frac{2}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{97.100}\right)\)
\(A=\frac{2}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{100}\right)\)
\(A=\frac{2}{3}.\left(1-\frac{1}{100}\right)\)
\(A=\frac{2}{3}.\frac{99}{100}=\frac{33}{50}\)
A = \(\frac{2}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{100}\right)\)
A = \(\frac{2}{3}.\left(1-\frac{1}{100}\right)\)= \(\frac{2}{3}.\frac{99}{100}\)= \(\frac{33}{50}\)
A = \(\frac{2}{1\cdot4}+\frac{2}{4\cdot7}+\frac{2}{7\cdot10}+....+\frac{2}{97\cdot100}\)
A = \(\frac{2}{3}\left(\frac{3}{1\cdot4}+\frac{3}{4\cdot7}+\frac{3}{7\cdot10}+....+\frac{3}{97\cdot100}\right)\)
A = \(\frac{2}{3}\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+....\frac{1}{97}-\frac{1}{100}\right)\)
A = \(\frac{2}{3}\left(\frac{1}{1}-\frac{1}{100}\right)\)
A = \(\frac{2}{3}\cdot\frac{99}{100}\)
A = \(\frac{33}{50}\)
Tính tổng: A = \(\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{97.100}\)
A=2/3(1-1/4+1/4-1/7+1/7-1/10+...+1/97-1/100)
A=2/3(1-1/100)
A=2/3.99/100
A=33/50
mình k pit co dung k nua nghe
A=2/1.4+2/4.7+2/7.10+...+2/97.100
=2/3(3/1.4+3/4.7+3/7.10+...+3/97.100)
=2/3(1-1/4+1/4-1/7+1/7-1/10+...+1/97-1/100)
=2/3(1-1/100)=33/50
Tìm x biết:
\(\left(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{97.100}\right)=\frac{0,33.x}{2009}\)
\(\left(\frac{1}{1.4}+\frac{1}{4.7}+...+\frac{1}{97.100}\right)=\frac{0,33x}{2009}\)
\(\left(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{97.100}\right)=\frac{0,33x}{2009}\)
\(\left(1-\frac{1}{4}+\frac{1}{4}-...-\frac{1}{100}\right)=\frac{0,33x}{2009}\)
\(1-\frac{1}{100}=\frac{0,33x}{2009}\)
\(\frac{99}{100}=\frac{0,33x}{2009}\Rightarrow2009x99=0,33x\times100\)
198891:100:0,33=6027=x
Tính tổng
\(B=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{97.100}\)
\(B=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{97.100}=\frac{2}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{97.100}\right)\)
\(=\frac{2}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{97}-\frac{1}{100}\right)=\frac{2}{3}\left(1-\frac{1}{100}\right)\)
\(=\frac{2}{3}.\frac{99}{100}=\frac{33}{50}\)
\(B=\frac{2}{1.4}+\frac{2}{4.7}+...+\frac{2}{97.100}=\frac{1}{3}\left(\frac{2}{1}-\frac{2}{4}+\frac{2}{4}-...-\frac{2}{100}\right)\)
\(B=\frac{1}{3}.\left(2-\frac{2}{100}\right)=\frac{1}{3}.\frac{99}{50}==\frac{33}{50}\)
Bạn ơi tớ hỏi Nguyễn Thiều Công Thành:
Vì sao lại = 2/3 . ( 3/1.4 + 3/4.7+ 3/7/10 + ... + 3/97.100 )
Tính tổng :
\(A=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{97.100}\)
\(\frac{3}{2}A=\frac{3}{2}\left(\frac{2}{1.4}+\frac{2}{4.7}+...+\frac{2}{97.100}\right)\)
\(\frac{3}{2}A=\frac{3}{2}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{100}\right)\)
\(\frac{3}{2}A=\frac{3}{2}\left(1-\frac{1}{100}\right)\)
\(\frac{3}{2}A=\frac{3}{2}\times\frac{99}{100}\)
\(A=\frac{99}{100}\)