số 2 đang bán bánh đa ở quận đống đa ~~~ mời số 3

số 2 đang hát mời số 3 

đề hơi sai, mk sửa lại nhé

Đặt \(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{98.99.100}\)

\(\Leftrightarrow2A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{98.99.100}\)

\(\Leftrightarrow2A=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{98.99}-\frac{1}{99.100}\)

\(\Leftrightarrow2A=\frac{1}{1.2}-\frac{1}{99.100}\)

\(\Leftrightarrow2A=\frac{4950}{9900}-\frac{1}{9900}\)

\(\Leftrightarrow2A=\frac{4949}{9900}\)

\(\Leftrightarrow A=\frac{4949}{9900}\div2\)

\(\Leftrightarrow A=\frac{9898}{9900}=\frac{4949}{4950}\)

\(A=2+22+...+222222222...2222\left(\text{50 chữ số 2}\right)\)

​\(\Leftrightarrow A=2\left(1+11+...+111111111...1111\right)\)​

\(\Leftrightarrow A=\frac{2}{9}\left(9+99+...+9999999999...99\right)\)

\(\Leftrightarrow A=\frac{2}{9}\left[\left(10-1\right)+\left(10^2-1\right)+...+\left(10^{50}-1\right)\right]\)

\(\Leftrightarrow A=\frac{2}{9}\left[\left(10+10^2+...+10^{50}\right)-50\right]\)

Đặt \(B=\left[\left(10+10^2+...+10^{50}\right)\right]\)

\(\Leftrightarrow10B=\left[\left(10^2+10^3+...+10^{51}\right)\right]\)

\(\Leftrightarrow10B-B=\left[\left(10^2+10^3+...+10^{51}\right)\right]-10-10^2-...-10^{50}\)

\(\Leftrightarrow10B-B=10^{51}-10\)

\(\Rightarrow A=\frac{2}{9}\left(10^{51}-10-50\right)\)

\(\Rightarrow A=\frac{2}{9}\left(10^{51}-60\right)\)

2n+1/n+1 có gt nguyên

<=>2n+2-1/n+1

      2(n+1)-1/n+1

      2-(1/n+1)

để 2n+1/n+1 có gt nguyên 

<=>1/n+1 có gt nguyên 

=>n+1 thuộc {+_1}

lm tiếp nhé

Cảm ơn bn nha

Nếu bn biết các câu khác thì giúp mk nhek

\(0,25.2\frac{1}{3}.30.0,5.\frac{8}{45}\)

\(=\frac{1}{4}.\frac{7}{3}.30.\frac{1}{2}.\frac{8}{45}\)

\(=\frac{14}{9}\)

\(0,25.2\frac{1}{3}.30.0,5.\frac{8}{45}\)

\(=0,25.\frac{7}{3}.30.0,5.\frac{8}{45}\)

\(=\frac{7}{12}.30.\frac{4}{45}\)

\(\frac{35}{2}.\frac{4}{45}\)

\(=\frac{14}{9}\)

x +x.5 = 24 

x.1 + x.5 =24

x.(1+5)=24

x.6=24

  x=24:6

   x=4

Kick nha ^^ 

\(x+x\times5=24\)

\(x\times1+x\times5=24\)

\(x\times\left(1+5\right)=24\)

\(x\times6=24\)

\(x=24:6\)

\(x=4\)