A=3+5+7+...+49

Số số hạng là (49-3):2+1=46:3+1=24 số

Tổng là (49+3)*24/2=52*12=624

=>\(B=\dfrac{4-624}{217}=\dfrac{-620}{217}=-\dfrac{20}{7}\)

\(\frac{4-3-5-7-...-49}{217}\)

\(\Rightarrow\frac{4-\left(3+5+7+...+49\right)}{217}\)

\(\Rightarrow\frac{4-[(49+3).[(49-3):2+1]:2]}{217}\)(Theo  Công Thức Tính Tổng)

\(\Rightarrow\frac{4-624}{217}\)

\(\Rightarrow\frac{-620}{217}\)

\(\Rightarrow\frac{-20}{7}\)

Chỗ phức tạp là ở biểu thức trong ngoặc thôi

Ta có

\(\dfrac{1}{8}+\dfrac{1}{8\cdot15}+\dfrac{1}{15\cdot22}...+\dfrac{1}{43\cdot50}\)

\(=\dfrac{1}{8}\cdot\left[\dfrac{1}{7}\left(\dfrac{1}{8}-\dfrac{1}{15}+\dfrac{1}{15}-\dfrac{1}{22}+....+\dfrac{1}{43}-\dfrac{1}{50}\right)\right]\)

\(=\dfrac{1}{8}\cdot\left[\dfrac{1}{7}\left(\dfrac{1}{8}-\dfrac{1}{50}\right)\right]=\dfrac{1}{8}\cdot\dfrac{3}{200}=\dfrac{3}{1600}\)

A = \(\left(\frac{1}{8}+\frac{1}{8.15}+\frac{1}{15.22}+...+\frac{1}{43.50}\right)\cdot\frac{4-3-5-7-...-49}{217}\)

A = \(\frac{1}{7}.\left(\frac{7}{1.8}+\frac{7}{8.15}+\frac{7}{15.22}+...+\frac{7}{43.50}\right)\cdot\frac{4-\left(3+5+7+...+49\right)}{217}\)

A = \(\frac{1}{7}.\left(1-\frac{1}{8}+\frac{1}{8}-\frac{1}{15}+\frac{1}{15}-\frac{1}{22}+...+\frac{1}{43}-\frac{1}{50}\right)\cdot\frac{4-\left(49+3\right)\left[\left(49-3\right):2+1\right]:2}{217}\)

A = \(\frac{1}{7}\cdot\left(1-\frac{1}{50}\right)\cdot\frac{4-52.24:2}{217}\)

A = \(\frac{1}{7}\cdot\frac{49}{50}\cdot\frac{4-624}{217}\)

A = \(\frac{7}{50}\cdot\frac{-620}{217}=-\frac{2}{5}\)

1: \(=\left(217-213+186\right)+\left(-14-49+54\right)\)

\(=190-9=181\)

2: \(=-38\cdot25+38\cdot4-25\cdot4+25\cdot38\)

\(=13\cdot4=52\)

3: \(=-39\cdot5+39\cdot99+99\cdot10-99\cdot39\)

\(=-195+990=795\)

4: =(1+3-5-7)+(9+11-13-15)+...+(393+395-397-399)

=(-8)+(-8)+...+(-8)

=-800

`@` `\text {Ans}`

`\downarrow`

`1,`

\(1+(-4)+7+(-10)+13\)

`= 1+(7+13)+(-4-10)`

`= 1+10-14`

`= 11-14`

`= -3`

`2, `

\(-2+7+(-12)+17+(-22)\)

`= -2+(7+17)+(-12-22)`

`= -2 + 24 - 24`

`= -2`

`3,`

\(44+45+46+47-24-25-26-27\)

`= (44 - 24)+(45 - 25) + (46 - 26)+(47 - 27)`

`= 20 + 20 + 20 + 20`

`= 40`

`4,`

\((-213)+186+(-14)+217+54+(-49)\)

`= (186 + 54)+(-213-14-49) + 217`

`= 240 - 276 + 217`

`= -36 + 217 = 181`