số kg đậu đen nấu chín là :

1,2 : 24 x 100 = 5 ( kg )

đáp số : 5 kg 

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\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x.\left(x+1\right):2}=\frac{2009}{2011}\)

\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x.\left(x+1\right)}=\frac{2009}{4022}\)(nhân mỗi vế với 1/2)

\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x.\left(x+1\right)}=\frac{2009}{4022}\)

\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2009}{4022}\)

\(\frac{1}{2}-\frac{1}{x+1}=\frac{2009}{4022}\)\(\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2009}{4022}=\frac{1}{2011}\)

\(\Rightarrow x+1=2011\Rightarrow x=2010\)

\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right):2}=\frac{2009}{2011}\)

\(\Rightarrow\frac{1}{2}\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right):2}\right)=\frac{2009}{4022}\)

\(\Rightarrow\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}=\frac{2009}{4022}\)

\(\Rightarrow\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{x\left(x+1\right)}\)\(=\frac{2009}{4022}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\)\(=\frac{2009}{4022}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2009}{4022}\)

\(\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2009}{4022}\)

\(\Rightarrow\frac{1}{x+1}=\frac{1}{2011}\)

\(\Rightarrow x+1=2011\)

\(\Rightarrow x=2010\)

\(\frac{1}{101}\)+ \(\frac{1}{102}\)+ \(\frac{1}{103}\)+ \(\frac{1}{150}>\frac{1}{150}+\frac{1}{150}+...+\frac{1}{150}=\frac{50}{150}=\frac{1}{3}\)

\(\frac{1}{151}+\frac{1}{152}+...+\frac{1}{200}>\frac{1}{200}+\frac{1}{200}+...+\frac{1}{200}=\frac{50}{200}=\frac{1}{4}\)

=> \(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{150}+\frac{1}{151}+...+\frac{1}{200}>\frac{1}{3}+\frac{1}{4}=\frac{7}{12}=\frac{6}{12}=\frac{1}{2}\)  (đpcm)

1/101+1/102+1/103+...+1/200>1/200x100=1/2

1/101+1/102+1/103+...+1/200>1/150x100=2/3

vì 2/3>1/2nên 1/101+1/102+1/103+...1/200>1/2 

3ⁿ⁺²+2ⁿ⁺³+3ⁿ+2ⁿ⁺¹ = (3ⁿ⁺² + 3ⁿ ) + (2ⁿ⁺³ + 2ⁿ⁺¹) = 3ⁿ. (3² + 1) + 2ⁿ. (2³ + 2¹) = 10.3ⁿ + 10. 2ⁿ

= 10. (3ⁿ + 2ⁿ) chia hết cho 10

=> đpcm

Đổi \(1\frac{3}{7}=\frac{10}{7}\)

Số đó là:

\(-5:\frac{10}{7}=\frac{-35}{10}=\frac{-7}{2}\)

\(1\frac{3}{7}\)=\(\frac{10}{7}\)

Tìm một số là:

\(-5\):\(\frac{10}{7}\)=\(\frac{-35}{10}\)=\(\frac{-7}{2}\)

     đáp số:\(\frac{-7}{2}\)

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