\(\dfrac{1}{55^2}\).\(5^4\).(-11)\(^2\) . \(55^5\) . (\(\dfrac{1}{5^2}\))\(^2\) : (\(5^3\) . \(11^6\)
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25 tháng 3 2022
\(\dfrac{1}{5}+\dfrac{2}{11}< \dfrac{x}{55}< \dfrac{2}{5}+\dfrac{1}{5}\)
\(\dfrac{11+10}{55}< \dfrac{x}{55}< \dfrac{3}{5}\)
\(\dfrac{21}{55}< \dfrac{x}{55}< \dfrac{33}{55}\)
Vậy \(x\in\left\{22;23;24;...\right\}\)
31 tháng 3 2023
\(=1-\dfrac{1}{2}+1-\dfrac{1}{6}+...+1-\dfrac{1}{90}\)
\(=10-\left(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{90}\right)\)
\(=10-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\)
=9+1/10
=9,1
BC
16 tháng 3 2022
Bài 3
\(\dfrac{55}{23}+\dfrac{-22}{23}\le x\le\dfrac{1}{5}-\dfrac{-1}{6}+\dfrac{79}{30}\)
\(=\dfrac{33}{23}\)\(\le x\le\dfrac{90}{30}\)
\(=\dfrac{33}{23}\le x\le3\)
Mà \(x\in Z\) \(\Rightarrow\)\(x=2\)
Có 1 giá trị thỏa mãn
Chọn A
Bài 4
\(\dfrac{-11}{12}< \dfrac{5}{x}< \dfrac{-11}{15}\)
Chọn D
Bài 5
\(M=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{99\cdot100}\)
\(M=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{99}+\dfrac{1}{99}-\dfrac{1}{100}\)
\(M=1-\dfrac{1}{100}\)
\(M=\dfrac{100}{100}-\dfrac{1}{100}\)
\(M=\dfrac{99}{100}\)
CHọn C
H
4 tháng 4 2021
\(A=\dfrac{1}{2}+\dfrac{5}{6}+\dfrac{11}{12}+\dfrac{29}{30}+\dfrac{41}{42}+\dfrac{55}{56}\\ =\left(1-\dfrac{1}{2}\right)+\left(1-\dfrac{1}{6}\right)+\left(1-\dfrac{1}{12}\right)+\left(1-\dfrac{1}{30}\right)+\left(1-\dfrac{1}{42}\right)+\left(1-\dfrac{1}{56}\right)\\ =6-\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}\right)\\ =6-\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{5\cdot6}+\dfrac{1}{6\cdot7}+\dfrac{1}{7\cdot8}\right)\\ 6-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}\right)\\ =6-\left(1-\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{8}\right)=\dfrac{207}{40}\)
Chắc đề thiếu, nhưng mình cứ làm hướng kiểu kia trước nhaa
4 tháng 4 2021
Giải:
1/2+ 5/6+ 11/12+ 29/30+ 41/42+ 55/56
=(1- 1/2)+ (1-1/6)+ (1- 1/12)+ (1-1/30)+ (1- 1/42)+ (1- 1/56)
=1- 1/2+ 1- 1/6+1-1/12 1-1/30+1-1/42+1-1/56
=6-(1/2+1/6+1-1/12+1/30+1/42+1/56)
=6-(1/1.2+1/2.3+1/3.4+1/5.6+1/6.7+1/7.8)
=6-(1/1-1/2+1/2-1/3+1/3-1/4+1/5-1/6+1/6-1/7+1/7-1/8)
=6-(1/1-1/4+1/5-1/8)
=6-33/40
=207/40
Chúc bạn học tốt!
27 tháng 4 2018
a)
\(\dfrac{1}{2\cdot3}x+\dfrac{1}{3\cdot4}x+...+\dfrac{1}{49\cdot50}x=1\\ x\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}\right)=1\\ x\left(\dfrac{1}{2}-\dfrac{1}{50}\right)=1\\ x\cdot\dfrac{12}{25}=1\\ x=1:\dfrac{12}{25}=1\cdot\dfrac{25}{12}=\dfrac{25}{12}\)
22 tháng 10 2021
Bài 1:
a) \(\dfrac{19}{12}+\left|\dfrac{-5}{2}\right|+\left(\dfrac{3}{2}\right)^2=\dfrac{19}{12}+\dfrac{5}{2}+\dfrac{9}{4}\)
\(=\dfrac{19+5.6+9.3}{12}=\dfrac{76}{12}=\dfrac{19}{3}\)
b) \(\dfrac{2}{11}.\dfrac{16}{9}-\dfrac{2}{11}.\dfrac{7}{9}=\dfrac{2}{11}\left(\dfrac{16}{9}-\dfrac{7}{9}\right)=\dfrac{2}{11}.1=\dfrac{2}{11}\)
Bài 2:
Áp dụng t/c dtsbn:
\(\dfrac{a}{8}=\dfrac{b}{3}=\dfrac{a-b}{8-3}=\dfrac{55}{5}=11\)
\(\Rightarrow\left\{{}\begin{matrix}x=11.8=88\\b=11.3=33\end{matrix}\right.\)
12 tháng 2 2022
Câu 1: A
Câu 2: C
Câu 3: 1/4 quả dưa nặng 0,5kg
Câu 4: =-3-1,3+5,6=4,3-3=1,3
\(\dfrac{1}{55^2}.5^4.\left(-11\right)^2.55^5.\left(\dfrac{1}{5^2}\right)^2:\left(5^3.11^6\right)\)
\(=\dfrac{5^4.11^2.5^5.11^5}{5^2.11^2}.\dfrac{1}{5^4.5^3.11^6}\)
\(=\dfrac{5^9.11^7}{5^9.11^8}=\dfrac{1}{11}\)
\(=\dfrac{1}{5^2\cdot11^2}\cdot5^4\cdot11^2\cdot55^5\cdot\left(\dfrac{1}{5}\right)^2\cdot\dfrac{1}{5^3\cdot11^6}\)
\(=5^2\cdot5^5\cdot11^5\cdot\dfrac{1}{5^2\cdot5^3\cdot11^6}\)
\(=\dfrac{11^5}{11^6}\cdot\dfrac{5^7}{5^5}=\dfrac{25}{11}\)