Tính nhanh \(A=1+\dfrac{1}{1+2}+\dfrac{1}{1+2+3}+...+\dfrac{1}{1+2+...+8}\)
Những câu hỏi liên quan
Bài 1. Tính nhanh giá trị của biểu thức sau:
a, E = \(\dfrac{1}{2}\)+ \(\dfrac{1}{3}\)+ \(\dfrac{1}{6}\)+ \(\dfrac{1}{24}\)+ \(\dfrac{1}{8}\)+ \(\dfrac{1}{2}\)+\(\dfrac{1}{12}\)
\(E=\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{8}+\dfrac{1}{2}+\dfrac{1}{12}\)
\(E=\left(\dfrac{1}{2}+\dfrac{1}{2}\right)+\left(\dfrac{1}{3}+\dfrac{1}{6}\right)+\left(\dfrac{1}{8}+\dfrac{1}{12}+\dfrac{1}{24}\right)\)
\(E=\dfrac{2}{2}+\dfrac{3}{6}+\left(\dfrac{1}{8}+\dfrac{3}{24}\right)\)
\(E=1+\dfrac{1}{2}+\left(\dfrac{1}{8}+\dfrac{1}{8}\right)\)
\(E=\left(\dfrac{2}{2}+\dfrac{1}{2}\right)+\dfrac{2}{8}\)
\(E=\dfrac{3}{2}+\dfrac{1}{4}\)
\(E=\dfrac{6}{4}+\dfrac{1}{4}\)
\(E=\dfrac{7}{4}\)
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a) tính nhanh
( 1 + \(\dfrac{1}{2}\) ) x ( 1 + \(\dfrac{1}{3}\) ) x ..... x ( 1 + \(\dfrac{1}{2005}\) )
b) tính bằng cách thuận tiện
\(\dfrac{2}{3}\) x \(\dfrac{1}{2}\) + \(\dfrac{1}{3}\) x \(\dfrac{1}{2}\)
a)\(=\left(\dfrac{2}{2}+\dfrac{1}{2}\right)\times\left(\dfrac{3}{3}+\dfrac{1}{3}\right)\times...\times\left(\dfrac{2005}{2005}+\dfrac{1}{2005}\right)\)
\(=\dfrac{3}{2}\times\dfrac{4}{3}\times...\times\dfrac{2006}{2005}=\dfrac{2006}{2}=1003\)
b)\(=\left(\dfrac{2}{3}+\dfrac{1}{3}\right)\times\dfrac{1}{2}=\dfrac{3}{3}\times\dfrac{1}{2}=\dfrac{1}{2}\)
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b)
\(\dfrac{1}{2}x\left(\dfrac{2}{3}+\dfrac{1}{3}\right)=\dfrac{1}{2}x1=\dfrac{1}{2}\)
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tính nhanh.
0.125*\(\dfrac{3}{7}\)-\(\dfrac{1}{8}\)*\(\dfrac{11}{7}\)
\(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{99\cdot100}\)
\(0,125.\dfrac{3}{7}-\dfrac{1}{8}.\dfrac{11}{7}=\dfrac{1}{8}.\dfrac{3}{7}-\dfrac{1}{8}.\dfrac{11}{7}=\dfrac{1}{8}\left(\dfrac{3}{7}-\dfrac{11}{7}\right)=\dfrac{1}{8}.-\dfrac{8}{7}=-\dfrac{1}{7}\)
\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{99.100}=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{99}-\dfrac{1}{100}=1-\dfrac{1}{100}=\dfrac{99}{100}\)
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27 tháng 5 2022 lúc 20:25
a. Tính nhanh: \(\dfrac{1}{1+2}+\dfrac{1}{1+2+3}+\dfrac{1}{1+2+3+4}+....+\dfrac{1}{1+2+3+...+10}\)
Tính nhanh :
\(\dfrac{1}{2}+\dfrac{-1}{3}+\dfrac{1}{4}+\dfrac{-1}{5}+\dfrac{1}{6}+\dfrac{-1}{7}+\dfrac{1}{8}+\dfrac{1}{7}+\dfrac{-1}{6}+\dfrac{1}{5}+\dfrac{-1}{4}+\dfrac{1}{3}+\dfrac{-1}{2}\)
Câu 2 : Tính nhanh:
\(\dfrac{1}{2}\)+\(\dfrac{1}{4}\)+\(\dfrac{1}{8}\)+...+\(\dfrac{1}{256}\)+\(\dfrac{1}{512}\)
Đặt \(A=\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+...+\dfrac{1}{256}+\dfrac{1}{512}\)
\(\Rightarrow2A=1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{128}+\dfrac{1}{256}\)
\(\Rightarrow A=2A-A=1+\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{128}+\dfrac{1}{256}-\dfrac{1}{2}-\dfrac{1}{4}-\dfrac{1}{8}-...-\dfrac{1}{256}-\dfrac{1}{512}\)
\(\Rightarrow A=1-\dfrac{1}{512}=\dfrac{511}{512}\)
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Đặt ⇒2A=1+12+14+...+1128+1256⇒2A=1+12+14+...+1128+1256
⇒A=1−1512=511512
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Tính nhanh:
a) 2.dfrac{3}{7}+left(dfrac{2}{9}-1dfrac{3}{7}right)-dfrac{5}{3}:dfrac{1}{9}
b) dfrac{-11}{23}.dfrac{6}{7}+dfrac{8}{7}.dfrac{-11}{23}-dfrac{1}{23}
c) left(dfrac{377}{-231}-dfrac{123}{89}+dfrac{34}{791}right).left(dfrac{1}{6}-dfrac{1}{8}-dfrac{1}{24}right)
d) 19dfrac{5}{8}:dfrac{7}{12}-15dfrac{1}{4}:dfrac{7}{12}
e) dfrac{2}{5}.dfrac{1}{3}-dfrac{2}{15}:dfrac{1}{5}+dfrac{3}{5}.dfrac{1}{3}
Đọc tiếp
Tính nhanh:
a) \(2.\dfrac{3}{7}+\left(\dfrac{2}{9}-1\dfrac{3}{7}\right)-\dfrac{5}{3}:\dfrac{1}{9}\)
b) \(\dfrac{-11}{23}.\dfrac{6}{7}+\dfrac{8}{7}.\dfrac{-11}{23}-\dfrac{1}{23}\)
c) \(\left(\dfrac{377}{-231}-\dfrac{123}{89}+\dfrac{34}{791}\right).\left(\dfrac{1}{6}-\dfrac{1}{8}-\dfrac{1}{24}\right)\)
d) \(19\dfrac{5}{8}:\dfrac{7}{12}-15\dfrac{1}{4}:\dfrac{7}{12}\)
e) \(\dfrac{2}{5}.\dfrac{1}{3}-\dfrac{2}{15}:\dfrac{1}{5}+\dfrac{3}{5}.\dfrac{1}{3}\)
tính nhanh
1+\(\dfrac{1}{2}+\dfrac{3}{4}+\dfrac{3}{6}+\dfrac{6}{8}\)
\(1+\dfrac{1}{2}+\dfrac{3}{4}+\dfrac{3}{6}+\dfrac{6}{8}\)
\(=1+(\dfrac{1}{2}+\dfrac{3}{6})+(\dfrac{3}{4}+\dfrac{6}{8})\)
\(=1+(\dfrac{3}{6}+\dfrac{3}{6})+(\dfrac{6}{8}+\dfrac{6}{8})\)
\(=1+1+1,5=3,5\)
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Tính nhanh:
\(25\%+\dfrac{3}{4}+\dfrac{1}{2}:0.5-\dfrac{1}{4}:0.25+\dfrac{1}{8}:0.125\)
`25%+3/4+1/2:0,5-1/4:0,15+1/8:0,125`
`=1/4+3/4+1/2xx2-1/4xx4+1/8xx8`
`(1/4+3/4)+(1/2xx2)-(1/4xx4)+(1/8xx8)`
`=1+1-1+1`
`=2`
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