Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
c)\(\left(1+\dfrac{1}{2}\right)\left(1+\dfrac{1}{3}\right)\left(1+\dfrac{1}{4}\right)....\left(1+\dfrac{1}{2020}\right)\left(1+\dfrac{1}{2021}\right)\)
\(=\left(\dfrac{1.2}{1.2}+\dfrac{1}{2}\right)\left(\dfrac{1.3}{1.3}+\dfrac{1}{3}\right)...\left(\dfrac{1.2021}{1.2021}+\dfrac{1}{2021}\right)\)
\(=\dfrac{3}{1.2}\cdot\dfrac{4}{1.3}\cdot\cdot\cdot\cdot\dfrac{2022}{1.2021}\)
\(=\dfrac{3.4.5...2022}{\left(1.1.1....1\right)\left(2.3.4...2021\right)}\)
\(=\)\(\dfrac{3.4.5...2022}{2.3.4...2021}\)
\(=\dfrac{2022}{2}=1011\)
\(d\))\(\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)....\left(1-\dfrac{1}{199}\right)\left(1-\dfrac{1}{200}\right)\)
\(=\left(\dfrac{2}{1.2}-\dfrac{1}{1.2}\right)\left(\dfrac{3}{1.3}-\dfrac{1}{1.3}\right)....\left(\dfrac{200}{1.200}-\dfrac{1}{1.200}\right)\)
\(=\dfrac{1.2.3....199}{\left(1.1.1....1\right).\left(2.3.4....200\right)}\)
\(=\dfrac{1.2.3...199}{2.3.4...200}\)
Nếu mik làm sai mong bạn thông cảm
`4 / 7 xx [-5] / 6 xx 7 / 4 xx 12 / 5`
`= [ 4 xx (-5) xx 7 xx 12 ] / [ 7 xx 6 xx 4 xx 5 ]`
`= [ 4 xx (-5) xx 7 xx 6 xx 2 ] / [ 7 xx 6 xx 4 xx 5 ]`
`= -2`
4/7 × -5/7 × 7/4 ×12/5
=> -10/21 × 42/10
=> -420/210
=> -42/21
Đáp số: -42/21
3:
1: Gọi chiều dài, chiều rộng lần lượt là a,b
Theo đề, ta có: 6/5a*4/5b=ab-30
=>ab=750
=>S=750
2:
Sau 1,5h thì xe 1 đi được 15*1,5=22,5(km)
Hiệu vận tốc là 20-15=5(km/h)
Thời gian hai xe đuổi kịp nhau là:
22,5/5=4,5(h)
=>Người 1 đi đến B sau 5h
ĐỘ dài AB là:
15*5=75km
Bài 2:
a) \(\dfrac{5}{6}:x=\dfrac{13}{9}\cdot\dfrac{3}{26}\)
\(\Rightarrow\dfrac{5}{6}:x=\dfrac{3}{9\cdot2}\)
\(\Rightarrow\dfrac{5}{6}:x=\dfrac{1}{6}\)
\(\Rightarrow x=\dfrac{5}{6}:\dfrac{1}{6}\)
\(\Rightarrow x=5\)
b) \(\dfrac{x-1}{21}=\dfrac{3}{x+1}\)
\(\Rightarrow\left(x-1\right)\left(x+1\right)=3\cdot21\)
\(\Rightarrow x^2-x+x-1=63\)
\(\Rightarrow x^2-1=63\)
\(\Rightarrow x^2-64=0\)
\(\Rightarrow x^2-8x+8x-64=0\)
\(\Rightarrow x\left(x-8\right)+8\left(x-8\right)=0\)
\(\Rightarrow\left(x+8\right)\left(x-8\right)=0\)
TH1: `x+8=0=>x=-8`
TH2: `x-8=0=>x=8`
c) \(2\dfrac{1}{2}x+x=2\dfrac{1}{17}\)
\(\Rightarrow\dfrac{5}{2}x+x=\dfrac{35}{17}\)
\(\Rightarrow x\cdot\left(\dfrac{5}{2}+1\right)=\dfrac{35}{17}\)
\(\Rightarrow x\cdot\dfrac{7}{2}=\dfrac{35}{17}\)
\(\Rightarrow x=\dfrac{35}{17}:\dfrac{7}{2}\)
\(\Rightarrow x=\dfrac{10}{17}\)
d) \(x-3\dfrac{1}{2}x=-2\dfrac{6}{7}\)
\(\Rightarrow x-\dfrac{7}{2}x=-\dfrac{20}{7}\)
\(\Rightarrow x\cdot\left(1-\dfrac{7}{2}\right)=\dfrac{-20}{7}\)
\(\Rightarrow x\cdot\dfrac{-5}{2}=\dfrac{-20}{7}\)
\(\Rightarrow x=\dfrac{-20}{7}:\dfrac{-5}{2}\)
\(\Rightarrow x=\dfrac{8}{7}\)
Bài 2:
a: \(\dfrac{5}{6}:x=\dfrac{13}{9}\cdot\dfrac{3}{26}\)
=>\(\dfrac{5}{6}:x=\dfrac{13}{26}\cdot\dfrac{3}{9}=\dfrac{1}{6}\)
=>\(x=\dfrac{5}{6}:\dfrac{1}{6}=\dfrac{5}{6}\cdot\dfrac{6}{1}=5\)
b:
ĐKXĐ: x<>-1
\(\dfrac{x-1}{21}=\dfrac{3}{x+1}\)
=>\(\left(x-1\right)\left(x+1\right)=3\cdot21\)
=>\(x^2-1=63\)
=>\(x^2=64\)
=>\(\left[{}\begin{matrix}x=8\left(nhận\right)\\x=-8\left(nhận\right)\end{matrix}\right.\)
c: \(2\dfrac{1}{2}\cdot x+x=2\dfrac{1}{17}\)
=>\(x\left(2,5+1\right)=\dfrac{35}{17}\)
=>\(x\cdot\dfrac{7}{2}=\dfrac{35}{17}\)
=>\(x=\dfrac{35}{17}:\dfrac{7}{2}=\dfrac{35}{17}\cdot\dfrac{2}{7}=\dfrac{10}{17}\)
d: \(x-3\dfrac{1}{2}x=-2\dfrac{6}{7}\)
=>\(x\left(1-3,5\right)=-\dfrac{20}{7}\)
=>\(x\cdot2,5=\dfrac{20}{7}\)
=>\(x=\dfrac{8}{7}\)