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a)x/5=32/80
=>80x=32*5
x=160/8
x=20
b)13/x=26/30
=>26x=13*30
x=390/26
x=15
c)-x/7=22/-77
=>(-x)*(-77)=22*7
x*77=154
x=154/77
x=2
1/21+1/28+1/36+...+2/[x.(x+1)]=2/9
=>2/42+2/56+2/72+...+2/[x.(x+1)]=2/9
=>2.(1/42+1/56+1/72+...+1/[x.(x+1)])=2/9
=>2.(1/6-1/7+1/7-1/8+1/8-1/9+...+1/x-1/(x+1))=2/9
=>1/6-1/(x+1)=1/9
=>1/(x+1)=1/18
=>x+1=18
=>x=17
Đặt \(A=\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{x.\left(x+1\right)}\)
\(\Rightarrow\frac{1}{2}A=\frac{1}{21.2}+\frac{1}{28.2}+\frac{1}{36.2}...+\frac{2}{x.\left(x+1\right).2}\)
\(\Rightarrow\frac{1}{2}A=\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+...+\frac{1}{x\left(x+1\right)}\)
\(\Rightarrow\frac{1}{2}A=\frac{1}{6.4}+\frac{1}{7.8}+\frac{1}{8.9}+...+\frac{1}{x\left(x+1\right)}\)
\(\Rightarrow\frac{1}{2}A=\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{x}-\frac{1}{x+1}\)
\(\Rightarrow\frac{1}{2}A=\frac{1}{6}-\frac{1}{x+1}\)
\(\Rightarrow A=\left(\frac{1}{6}-\frac{1}{x+1}\right):\frac{1}{2}\)
Theo bài ra ta có :
\(\left(\frac{1}{6}-\frac{1}{x+1}\right):\frac{1}{2}=\frac{2}{9}\)
\(\Rightarrow\frac{1}{6}-\frac{1}{x+1}=\frac{2}{9}.\frac{1}{2}\)
\(\frac{1}{6}-\frac{1}{x+1}=\frac{2}{18}\)
\(\frac{1}{x+1}=\frac{1}{6}-\frac{2}{18}\)
\(\frac{1}{x+1}=\frac{3}{18}-\frac{2}{18}\)
\(\frac{1}{x+1}=\frac{1}{18}\)
\(\Rightarrow x+1=18\)
\(\Rightarrow x=18-1\)
\(\Rightarrow x=17\)
Vậy x = 17
\(\Rightarrow\frac{x+10}{490}+\frac{x+20}{480}+\frac{x+30}{470}+\frac{x+40}{460}+\frac{x+50}{450}+5=0\)
\(\Rightarrow\frac{x+10}{490}+1+\frac{x+20}{480}+1+\frac{x+30}{470}+1+\frac{x+40}{460}+1+\frac{x+50}{450}+1=0\)
\(\Rightarrow\frac{x+500}{490}+\frac{x+500}{480}+\frac{x+500}{470}+\frac{x+500}{460}+\frac{x+500}{450}=0\)
\(\Rightarrow\left(x+500\right).\left(\frac{1}{490}+\frac{1}{480}+\frac{1}{470}+\frac{1}{460}+\frac{1}{450}\right)=0\Rightarrow x+500=0\Rightarrow x=-500\)
a)11 3/13-(2 4/7+5 3/13)=11+3/13-(2+4/7+5+3/13)=11+3/13-2-4/7-5-3/13=(11-2-5)+(3/13-4/7-3/13)=4+(0-4/7)=4+-4/7=28/7-4/7=28-4/7=24/7=3 3/7(phải tính ta hỗn số nha bn)
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\(\text{}\text{}11\frac{3}{13}-\left(2\frac{4}{7}+5\frac{3}{13}\right)=11\frac{3}{13}-2\frac{4}{7}-5\frac{3}{13}=11\frac{3}{13}-5\frac{3}{13}-2\frac{4}{7}=6-2\frac{4}{7}=5\frac{7}{7}-2\frac{4}{7}=3\frac{3}{7}\)
Ta có:
\(4\left(1+5+5^2+...+5^9\right)=5\left(1+5+5^2+...+5^9\right)-\left(1+5+5^2+...+5^9\right)\)
\(=5+5^2+5^3+...+5^{10}-1-5-5^2-...-5^9\)
\(=5^{10}-1+\left(5-5\right)+\left(5^2-5^5\right)+..+\left(5^9-5^9\right)\)
\(=5^{10}-1\)
=> \(1+5+5^2+...+5^9=\frac{5^{10}-1}{4}\)
Tương tự: \(1+5+5^2+...+5^8=\frac{5^9-1}{4}\)
\(1+3+3^2+...+3^9=\frac{3^{10}-1}{2}\)
\(1+3+3^2+...+3^8=\frac{3^9-1}{2}\)
=> \(A=\frac{5^{10}-1}{5^9-1}>\frac{5^{10}-1}{5^9}=5-\frac{1}{5^9}>4;\)
\(B=\frac{3^{10}-1}{3^9-1}< \frac{3^{10}}{3^9-1}=3+\frac{3}{3^9-1}< 4;\)
=> A > B.
a. Ta có 333/444 = 333:111/444:111=3/4
tick đi mình làm tiếp cho