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a) \(\dfrac{1}{1\times3}+\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+...+\dfrac{1}{x\times\left(x+3\right)}=\dfrac{99}{200}\)
Ta có: \(\left(1-\dfrac{1}{3}\right)\times\dfrac{1}{2}+\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\times\dfrac{1}{2}+\left(\dfrac{1}{5}-\dfrac{1}{7}\right)\times\dfrac{1}{2}+...+\left(\dfrac{1}{x}-\dfrac{1}{x+3}\right).\dfrac{1}{2}=\dfrac{99}{200}\)
\(\dfrac{1}{2}\times\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{x}-\dfrac{1}{x+3}\right)=\dfrac{99}{200}\)
\(\dfrac{1}{2}\times\left(1-\dfrac{1}{x+3}\right)=\dfrac{99}{200}\)
\(1-\dfrac{1}{x+3}=\dfrac{99}{200}:\dfrac{1}{2}\)
\(1-\dfrac{1}{x+3}=\dfrac{99}{100}\)
\(\dfrac{1}{x+1}=1-\dfrac{99}{100}\)
\(\dfrac{1}{x+1}=\dfrac{1}{100}\)
\(\Rightarrow x+1=100\)
\(x=100-1\)
\(x=99\)
a) 10 x 18/27 x 15
= 2 x 5 x 2 x 9/3 x 9 x 3 x 5
= 4/9.
b) 1 x 2 x 3 x 4 x 5 x 6/7 x 8 x 9
= 1 x 2 x 3 x 4 x 5 x 3 x 2/7 x 2 x 4 x 3 x 3
= 1 x 5 x 2/ 7
= 10/7
c)\(1\frac{1}{2}.1\frac{1}{3}.1\frac{1}{4}.1\frac{1}{5}\)
\(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}.\frac{6}{5}\)
\(=3\)
d) \(1\frac{1}{2}:1\frac{1}{3}:1\frac{1}{4}:1\frac{1}{5}=\frac{3}{2}:\frac{4}{3}:\frac{5}{4}:\frac{6}{5}=\frac{3}{2}.\frac{3}{4}.\frac{4}{5}.\frac{5}{6}=\frac{3}{4}\)
2. a) 0,123; 0,132; 0,213; 0,231; 0,312; 0,321.
b) 0,321; 0,312; 0,231; 0,213; 0,132; 0,123
3. 5 số đó là; 0,11;0,12;0,13;0,14;0,15
a) 0,11;0,12;0,13;0,14;0,15
b) 0,15;0,14;0,13;0,12;0,11
a: -10/8<-1
-19/19=-1
-1<-2/10<0
0<5/12<1<17/15
=>17/15>1>5/12>-2/10>-19/19>-10/8
b: -1/3=-4/12; -5/12=-5/12; -3/4=-9/12; -1/4=-3/12; -7/12=-7/12
=>-3/4<-7/12<-5/12<-1/3<-1/4
sửa đề câu a và câu b nhá , mik nghĩ đề như này :
\(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{213\cdot215}\)
\(=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{213}-\frac{1}{215}\)
= \(\frac{1}{1}-\frac{1}{215}\)
\(=\frac{214}{215}\)
b, đặt \(A=\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+...+\frac{1}{213\cdot215}\)
\(A\cdot2=\frac{2}{1\cdot3}+\frac{2}{3.5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{213\cdot215}\)
\(A\cdot2=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{213}-\frac{1}{215}\)
\(A\cdot2=\frac{1}{1}-\frac{1}{215}\)
\(A\cdot2=\frac{214}{215}\)
\(A=\frac{214}{215}:2\)
\(A=\frac{107}{215}\)
CÁC SỐ VIẾT THEO THỨ TỰ TỪ BÉ ĐẾN LỚN LÀ : 1/5 ; 1/4 ; 1/3 ; 3/2
