150 x 1 + 150 x 2 + 150 x 3 +...+ 150 x 99 + 150 x 100

= 150 x ( 1 + 2 + 3 + ... + 99 + 100 )

= 150 x 5050 = 757500

  B = 150 x 1 + 150 x 2 + 150 x 3 + ... + 150 x 99 + 150 x 100

B = 150 x (1 + 2 + 3+... + 99 + 100)

Đặt:  A = 1 + 2 + 3 +...+ 100

Dãy số trên là dãy số cách đều với khoảng cách là:

         2 - 1 = 1

Số số hạng của dãy số trên là:

      (100 - 1) : 1 + 1 =  100 (số hạng)

A = (100 + 1) x 100 : 2 = 5050

B = 150 x 5050

B = 757500 

150x150x150=3375000

150 x 150 x 150 = 3375000

150 x 150 x 150 = 3375000 nha

tk nhé

kb nữa

C

C

C

\(\left(\frac{x+4}{2000}+1\right)+\left(\frac{x+3}{2001}+1\right)-\left(\frac{x+2}{2002}+1\right)-\left(\frac{x+1}{2003}+1\right)=0\)

\(\frac{x+2004}{2000}+\frac{x+2004}{2001}-\frac{x+2004}{2002}-\frac{x+2004}{2003}=0\)

\(\left(x+2004\right).\left(\frac{1}{2000}+\frac{1}{2001}-\frac{1}{2002}-\frac{1}{2003}\right)=0\)

Vì \(\frac{1}{2000}>\frac{1}{2001}>\frac{1}{2002}>\frac{1}{2003}\)

=>\(x+2004=0\)

=>\(x=-2004\)

a, Ta có \(\frac{x+1}{10}+\frac{x+1}{11}+\frac{1+1}{12}=\frac{x+1}{13}+\frac{x+1}{14}\)

       =>  \(\left(x+1\right).\left(\frac{1}{10}+\frac{1}{11}+\frac{1}{12}\right)=\left(x+1\right).\left(\frac{1}{13}+\frac{1}{14}\right)\)

      =>   \(\left(x+1\right).\frac{181}{660}=\left(x+1\right).\frac{27}{182}\)

      =>    \(x.\frac{181}{660}+\frac{181}{660}=x.\frac{27}{182}+\frac{27}{182}\)

      =>   \(x\frac{181}{660}-x\frac{27}{182}=\frac{27}{182}-\frac{181}{660}\) 

      =>   \(x\frac{7561}{60060}=-\frac{7561}{60060}\)

     =>  x = -1

Mk chỉ biết cách làm này thôi mặc dù có cách khác nữa ( bạn thông càm ) 

Tích cho mk nhé

a)\(pt\Leftrightarrow-\frac{x}{2x^2-5}-\frac{25}{2x^2-50}+\frac{x}{x^2-5}+\frac{5}{x^2-5}=\frac{x}{2x^2+10x}-\frac{5}{2x^2+10x}\)

=>\(-\frac{x}{2x^2+10x}+\frac{5}{2x^2+10x}-\frac{x}{2x^2-50}-\frac{25}{2x^2-50}+\frac{x}{x^2-5}+\frac{5}{x^2-5}=0\)

\(\Leftrightarrow-\frac{5\left(x^2+8x-5\right)}{2\left(x-5\right)x\left(x^2-5\right)}=0\)

\(\Rightarrow\frac{1}{x-5}=0\Leftrightarrow\frac{1}{x}=0\Rightarrow\frac{1}{x^2-5}=0\)

=>x²+8x-5=0

=>8²-(-4(1.5))=84

=>x₁=(-8)+8:2=\(\sqrt{21}-4\)

=>x₂=(-8)+8:2=\(-\sqrt{21}-4\)

=>x=±\(\sqrt{21}-4\)

b)\(\Leftrightarrow-\frac{x}{x+1}+\frac{1}{x+1}+\frac{x}{x-1}+\frac{1}{x-1}=\frac{16}{x^2-1}\)

\(\Rightarrow-\frac{16}{x^2-1}-\frac{x}{x+1}+\frac{1}{x+1}+\frac{x}{x-1}+\frac{1}{x-1}=0\)

\(\Rightarrow\frac{4\left(x-4\right)}{\left(x-1\right)\left(x+1\right)}=0\Leftrightarrow\frac{1}{x-1}=0\Rightarrow\frac{1}{x+1}=0\)

=>x=4

c)\(\Leftrightarrow-\frac{x^2}{x+1}-\frac{x}{x+1}+\frac{2}{x+1}+x+2=\frac{x}{x+1}-\frac{1}{x+1}+\frac{x}{x-1}+\frac{1}{x-1}\)

\(\Rightarrow-\frac{x^2}{x+1}-\frac{2x}{x+1}+\frac{3}{x+1}-\frac{x}{x-1}+x-\frac{1}{x-1}+2=0\)

\(\Rightarrow\frac{2\left(x-3\right)}{\left(x-1\right)\left(x+1\right)}=0\Leftrightarrow\frac{1}{x-1}=0\Rightarrow\frac{1}{x+1}=0\)

=>x=3

Tách riêng thánh hai nhóm (x+x+x+...+x)+(1+4+7+10+...+28)=10x+145=156. Vậy x=11/10

\(\left(x+1\right)+\left(x+4\right)+...........+\left(x+28\right)=156\)

\(\Rightarrow x+1+x+4+..........+x+28=156\)

\(\Rightarrow10x+\left(1+4+.........+28\right)=156\)

\(\Rightarrow10x+145=156\)

\(\Rightarrow10x=11\)

\(\Rightarrow x=1,1\)

x = 1,1 nha bạn