Tính nhanh :
a> 1 + 4 + 7 + ... + 304
b> 1 + 5 + 9 + ... + 481
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a: \(=\left(\dfrac{4}{9}+\dfrac{5}{9}\right)+\left(\dfrac{1}{8}+\dfrac{7}{8}\right)=1+1=2\)
b: \(=\left(\dfrac{1}{6}+\dfrac{4}{6}+\dfrac{7}{6}\right)+\left(\dfrac{5}{12}+\dfrac{7}{12}\right)=2+1=3\)
c/
C = 1/100-1/100-1/99-1/99-1/98-1/98-1/97-..........-1/3-1/2-1/2-1/1
C = 1/100-1/100-1/1
C = 0-1/1
C = -1
a: \(=\dfrac{4}{5}\cdot\dfrac{7}{3}\cdot\dfrac{3}{7}\cdot\dfrac{5}{4}+2011=2011+1=2012\)
b: \(=\dfrac{1}{3}\cdot\dfrac{9}{7}\cdot\dfrac{7}{9}=\dfrac{1}{3}\)
\(A=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{9.11}-\frac{1}{11.13}\)
\(\Leftrightarrow A=\frac{1}{1.3}-\frac{1}{11.13}=\frac{1}{3}-\frac{1}{143}=\frac{140}{429}\)
\(A=\frac{4}{1.3.5}+\frac{4}{3.5.7}+\frac{4}{5.7.9}+\frac{4}{7.9.11}+\frac{4}{9.11.13}\)
\(\Rightarrow A=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{9.11}-\frac{1}{11.13}\)
\(\Rightarrow A=\frac{1}{1.3}-\frac{1}{11.13}=\frac{1}{3}-\frac{1}{143}=\frac{140}{429}\)
`!`
\(a,\dfrac{8}{9}\times\dfrac{7}{5}-\dfrac{7}{9}\times\dfrac{2}{5}+\dfrac{2}{9}\\ =\dfrac{8}{9}\times\left(\dfrac{7}{5}-\dfrac{2}{5}\right)+\dfrac{2}{9}\\ =\dfrac{8}{9}\times\dfrac{5}{5}+\dfrac{2}{9}\\ =\dfrac{8}{9}+\dfrac{2}{9}\\ =\dfrac{10}{9}\)
\(b,\dfrac{5}{9}\times\dfrac{1}{4}+\dfrac{4}{9}\times\dfrac{3}{12}\\ =\dfrac{5}{9}\times\dfrac{1}{4}+\dfrac{4}{9}\times\dfrac{1}{4}\\ =\dfrac{1}{4}\times\left(\dfrac{5}{9}+\dfrac{4}{9}\right)\\ =\dfrac{1}{4}\times\dfrac{9}{9}\\ =\dfrac{1}{4}\)
a: =-1/3+1/3=0
b: \(=\dfrac{4}{11}\left(-\dfrac{2}{7}-\dfrac{4}{7}-\dfrac{1}{7}\right)=\dfrac{4}{11}\cdot\left(-1\right)=-\dfrac{4}{11}\)
c: \(=10+\dfrac{5}{9}-3-\dfrac{5}{7}-4-\dfrac{5}{9}=3-\dfrac{5}{7}=\dfrac{16}{7}\)
d: \(=\dfrac{1}{3}+\dfrac{7}{4}-\dfrac{7}{4}+\dfrac{4}{5}=\dfrac{1}{3}+\dfrac{4}{5}=\dfrac{5+12}{15}=\dfrac{17}{15}\)
a: =-1/3+1/3=0
b: =411(−27−47−17)=411⋅(−1)=−411=411(−27−47−17)=411⋅(−1)=−411
c: =10+59−3−57−4−59=3−57=167=10+59−3−57−4−59=3−57=167
d: =13+74−74+45=13+45=5+1215=1715