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ta có: a=32.53-31=(31+1).53-31=31.53+53-31=53.31+22
vì 22<32 nên 53.31+22 <53.31+32
Gọi số hạng thứ 100 là x, khi đó ta có:
100 = ( x-2 ) : 3 + 1
=> x = 2 + (100 - 1 ) x 3
= 2 + 99 x 3
= 2 + 297
= 299
\(1-\frac{3}{2.10}-\frac{3}{4.15}-\frac{3}{6.20}-\frac{3}{8.25}-...-\frac{3}{198.500}\)
\(=1-\left(\frac{3}{2.10}+\frac{3}{4.15}+\frac{3}{6.20}+...+\frac{3}{198.500}\right)\)
\(=1-\frac{3}{2.5}.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)\)
\(=1-\frac{3}{10}.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\right)\)
\(=1-\frac{3}{10}.\left(1-\frac{1}{100}\right)\)
\(=1-\frac{3}{10}.\frac{99}{100}\)
\(=1-\frac{297}{1000}\)
\(=\frac{703}{1000}\)
P/s : Không biết đúng hông nha, làm đại
\(a,\frac{-7}{25}.\frac{11}{13}+\frac{-7}{25}.\frac{2}{13}-\frac{18}{25}\)
\(=\frac{-7}{25}.\left(\frac{11}{13}+\frac{2}{13}\right)-\frac{18}{25}=\frac{-7}{25}-\frac{18}{25}=-1\)
\(b,\frac{5}{7}.\frac{1}{3}-\frac{5}{7}.\frac{1}{4}-\frac{5}{7}.\frac{1}{12}=\frac{5}{7}.\left(\frac{1}{3}-\frac{1}{4}-\frac{1}{12}\right)=\frac{5}{7}.\left(\frac{4}{12}-\frac{3}{12}-\frac{1}{12}\right)\)
\(=\frac{5}{7}.0=0\)
c)\(5\frac{2}{5}.4\frac{2}{7}+5\frac{5}{7}.5\frac{2}{5}=\frac{27}{5}.\frac{30}{7}+\frac{40}{7}.\frac{27}{5}=\frac{27}{5}.\left(\frac{30}{7}+\frac{40}{7}\right)\)
\(=\frac{27}{5}.10=27.2=54\)
\(d,75\%-1\frac{1}{2}+0,5:\frac{5}{12}-\left(\frac{-1}{2}\right)^2=\frac{3}{4}-\frac{3}{2}+\frac{1}{2}.\frac{12}{5}-\frac{1}{4}\)
\(=\left(\frac{3}{4}-\frac{1}{4}\right)-\frac{3}{2}+\frac{6}{5}=\frac{1}{2}-\frac{3}{2}+\frac{6}{5}=-1+\frac{6}{5}=\frac{-5}{5}+\frac{6}{5}=\frac{1}{5}\)
Bài 1:
a) Ta có: \(\frac{7}{8}\cdot\frac{4}{9}+\frac{1}{14}:\frac{5}{14}\)
\(=\frac{28}{72}+\frac{1}{14}\cdot\frac{14}{5}\)
\(=\frac{28}{72}+\frac{1}{5}\)
\(=\frac{140}{360}+\frac{72}{360}\)
\(=\frac{212}{360}=\frac{53}{90}\)
Bài 2:
a) Ta có: \(\frac{2}{3}x+\frac{1}{4}x=\frac{-22}{27}\)
\(\Leftrightarrow x\cdot\left(\frac{2}{3}+\frac{1}{4}\right)=\frac{-22}{27}\)
\(\Leftrightarrow x\cdot\frac{11}{12}=\frac{-22}{27}\)
\(\Leftrightarrow x=\frac{-22}{27}:\frac{11}{12}=\frac{-22}{27}\cdot\frac{12}{11}=-\frac{8}{9}\)
Vậy: \(x=\frac{-8}{9}\)
\(\dfrac{-7}{13}\) + \(\dfrac{-5}{3}\) = \(\dfrac{-21}{39}\) + \(\dfrac{-65}{39}\) = \(\dfrac{-86}{39}\)
\(\frac{29\cdot18-29\cdot7}{28\cdot33+33}=\frac{29\cdot\left(18-7\right)}{\left(28+1\right)\cdot33}=\frac{29\cdot11}{29\cdot33}=\frac{11}{33}=\frac{1}{3}\)
Ta có: (- 476) - 53 = (-476) + (-53) = - ( 476 + 53) = - 529
Chọn đáp án (C) (-529).