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\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\)
\(=\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(=\frac{1}{2}+\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{1}{4}-\frac{1}{4}\right)+\left(\frac{1}{5}-\frac{1}{5}\right)-\frac{1}{6}\)
\(=\frac{1}{2}-\frac{1}{6}\)
\(=\frac{1}{3}\)
Đặt \(A=\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}\)
\(A=\frac{3-2}{2x3}+\frac{4-3}{3x4}+\frac{5-4}{4x5}+\frac{6-5}{5x6}\)
\(A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(A=\frac{1}{2}-\frac{1}{6}\)
\(A=\frac{3}{6}-\frac{1}{6}\)
\(A=\frac{2}{6}=\frac{1}{3}\)
1+2+3+4+5+6+7+8+9:9
=1+2+3+4+5+6+7+8+1
=(1+1)+(2+8)+(3+7)+(4+6)+5
=2+10+10+10+5
=(2+5)+(10+10+10)
=7+30
=37
Ta có:
\(\frac{1212}{2424}=\frac{1}{2}\)
\(\Rightarrow2018.\left(\frac{1}{2}+\frac{1}{2}\right)=2018.1=2018\)
a) 25 + 69 + 75 + 11
= (25 + 75) + (69 + 11)
= 100 + 80
= 180
b) 64 x 867 + 36 x 867
= (64 + 36) x 867
= 100 x 867
= 86700
c) 25 x 989 x 4 + 25
= 25 x 4 x 989 + 25
= 100 x 989 + 25
= 98900 + 25
= 98925
\(\dfrac{12}{7}\) \(\times\) \(\dfrac{3}{4}\) - \(\dfrac{3}{4}\) \(\times\) \(\dfrac{12}{7}\)
= \(\dfrac{9}{7}\) - \(\dfrac{9}{7}\)
= 0