1\(\frac{1}{12}-\frac{1}{20}-...-\frac{1}{380}=?\)
Những câu hỏi liên quan
Tìm x biết
a,
\(|x-1|+|x-2|+|x-3|=2\)
b,
\(|3x+\frac{1}{2}|+|3x+\frac{1}{6}|+|3x+\frac{1}{12}|+|3x+\frac{1}{20}|+...+|3x+380|=58x\)
Đặt bt trên là A nha
Đổi |x-1|=|1-x|
Suy ra A=|1-x|+x-2|+|x-3|
Áp dụng BĐTGTTĐ ta có
A=|1-x|+x-2|+|x-3|\(\ge\)|1-x+x-3|=2
Dấu = xảy ra khi \(\hept{\begin{cases}x-2=0\\1< x< 3\end{cases}}\)đồng thời xảy ra
Vậy x =2
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b,
\(\left|3x+\frac{1}{2}\right|\ge0\)
\(\left|3x+\frac{1}{6}\right|\ge0\)
..........
\(\left|3x+380\right|\ge0\)
Suy ra đề bài \(\ge\)0
suy ra 58x \(\ge\)0
Suy ra \(3x+\frac{1}{2}+3x+\frac{1}{6}+......+3x+380=58x\)
Tự tính nhé hok tốt
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\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+......+\frac{1}{380}\)= ?
1/2x3 + 1/3x4 +1/4x5+ ....+ 1/380 = ?
1/2.3+1/3.4+1/4.5+...+1/380
=1/2.3+1/3.4+1/4.5+...+1/19.20
=1/2-1/3+1/3-1/4+1/4-1/5+...+1/19-1/20
=1/2-1/20
=9/20
tick nha bn cám ơn
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\(A=\frac{3}{2}+\frac{3}{6}+\frac{3}{12}+\frac{3}{20}+...+\frac{3}{380}\)
A=3.(1/2 +1/6 +1/12 +1/20+...+1/380)
A:3=1/1.2+1/2.3+1/3.4 +...+1/19.20
A:3=1-1/20
A:3=19/20
A=19/20.3
A=57/20
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A=3/1X2+3/2X3+3/3X4+3/4X5+...+3/19X20
A=3(1/1X2+1/2X3+1/3X4+1/4X5+..+1/19X20
A=3(1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/19-1/20)
A=3(1/1-1/20)
A=3.19/20
A=57/20
tk cho mk nha
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A= \(\frac{3}{2}\)+ \(\frac{3}{6}\)+ \(\frac{3}{12}\)+....+ \(\frac{3}{380}\)
A= \(\frac{3}{1.2}\)+ \(\frac{3}{2.3}\)+ \(\frac{3}{3.4}\)+....+ \(\frac{3}{19.20}\)
A= \(\frac{3}{1}\)- \(\frac{3}{2}\)+ \(\frac{3}{2}\)- \(\frac{3}{3}\)+....+ \(\frac{3}{19}\)- \(\frac{3}{20}\)
A= \(\frac{3}{1}\)- \(\frac{3}{20}\)
A= \(\frac{57}{20}\)
Vậy A= \(\frac{57}{20}\)
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19 tháng 8 2019 lúc 11:16
e,Afrac{1}{2}+frac{5}{6}+frac{11}{12}+frac{19}{20}+frac{29}{30}+frac{41}{42}left(1-frac{1}{2}right)+left(1-frac{1}{6}right)+left(1-frac{1}{12}right)+left(1-frac{1}{20}right)+left(1-frac{1}{20}right)+left(1-frac{1}{42}right)Rightarrow A1-frac{1}{2}+1-frac{1}{6}+1-frac{1}{12}+1-frac{1}{20}+1-frac{1}{30}+1-frac{1}{42}4-left(frac{1}{2}+frac{1}{6}+frac{1}{12}+frac{1}{20}+frac{1}{30}+frac{1}{42}right)Rightarrow A4-left(frac{1}{1.2}+frac{1}{2.3}+frac{1}{3.4}+frac{1}{4.5}+frac{1}{5.6}+frac{1}{6.7}right)...
Đọc tiếp
e,\(A=\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}=\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+\left(1-\frac{1}{12}\right)+\left(1-\frac{1}{20}\right)+\left(1-\frac{1}{20}\right)+\left(1-\frac{1}{42}\right)\)
\(\Rightarrow A=1-\frac{1}{2}+1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+1-\frac{1}{30}+1-\frac{1}{42}=4-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)\)
\(\Rightarrow A=4-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)=4-\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)
\(\Rightarrow A=4-\left(\frac{1}{1}-\frac{1}{7}\right)=4-\frac{6}{7}=3\frac{1}{7}\)
BN mún hỏi j vậy, đây k phải câu hỏi, mà có thì phải là toán lớp 6
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Tính
\(1-\frac{1}{90}-\frac{1}{72}-\frac{1}{52}-\frac{1}{42}-\frac{1}{30}-\frac{1}{20}-\frac{1}{20}-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)
\(1-\frac{1}{90}-\frac{1}{72}-\frac{1}{56}-\frac{1}{42}-\frac{1}{30}-\frac{1}{20}-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)
\(=1-\left(\frac{1}{90}+\frac{1}{72}+\frac{1}{56}+\frac{1}{42}+\frac{1}{30}+\frac{1}{20}+\frac{1}{12}+\frac{1}{6}+\frac{1}{2}\right)\)
\(=1-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{90}\right)\)
\(=1-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\right)\)
\(=1-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(=1-\left(1-\frac{1}{10}\right)\)
\(=1-\frac{9}{10}\)
\(=\frac{1}{10}\)
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$\frac{1}{11}$ + $\frac{1}{12}$ + $\frac{1}{13}$ + ... + $\frac{1}{20}$ với $\frac{1}{2}$
tính thuận tiện : \(\frac{1}{12}+\frac{2}{7}+\frac{9}{12}+\frac{5}{7}+\frac{2}{12}+\frac{10}{20}+\frac{9}{20}+\frac{1}{12}=\)
=( 1/12+9/12+2/12+1/12) + ( 2/7+5/7) + (10/20+9/20)
= 13/12 +1+19/20
đến đây bạn tự tính nha
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ghép mẫu 12 vs 12 20 vs 20 rồng cộng lại
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Xem thêm câu trả lời
Tính nhanh:
A=\(\frac{1}{90}-\frac{1}{72}-\frac{1}{56}-\frac{1}{42}-\frac{1}{30}-\frac{1}{20}-\frac{1}{12}-\frac{1}{6}-\frac{1}{2}\)
B=\(\frac{3}{2}-\frac{5}{6}+\frac{7}{12}-\frac{9}{20}+\frac{11}{30}-\frac{13}{42}+\frac{15}{56}-\frac{17}{72}\)
A = \(\frac{-79}{90}\)
B = \(\frac{8}{9}\)
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Chứng minh rằng :
\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{19}-\frac{1}{20}=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{20}\)
Ta xét : \(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{19}-\frac{1}{20}=\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{19}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{20}\right)\)
\(=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{20}\right)-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+....+\frac{1}{20}\right)\)
\(=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{20}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{9}+\frac{1}{10}\right)\)
\(=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+....+\frac{1}{20}\)
Vì \(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+....+\frac{1}{20}=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{20}\)
nên \(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{19}-\frac{1}{20}=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+....+\frac{1}{20}\) ( đpcm )
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