500 × 4 × 2 × 25 - 500 × 3 × 2 × 30

= 500 × (4 × 2 × 25) - 500 × (3 × 2 × 30)

= 500 × 200 - 500 × 180

= 500 × (200 - 180)

= 500 × 20

= 10000

\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+30\right)=500\)

Số lượng số hạng là: \(30-1+1=30\)

\(\Rightarrow30x+\dfrac{30\left(30+1\right)}{2}=500\)

\(30x+465=500\)

\(30x=35\)

\(x=\dfrac{7}{6}\)

\(\left(x+1\right)+\left(x+2\right)+...+\left(x+30\right)=500\)

\(\Rightarrow x+1+x+2+..+x+30=500\)

\(\Rightarrow\left(x+x+...+x\right)+\left(1+2+...+30\right)=500\)

\(\Rightarrow30\cdot x+465=500\)

\(\Rightarrow30\cdot x=500-465\)

\(\Rightarrow30\cdot x=35\)

\(\Rightarrow x=\dfrac{35}{30}\)

\(\Rightarrow x=\dfrac{7}{6}\)

GIÚP MÌNH VỚI Ạ 

(x + 1) + (x + 2) + (x + 3) + ... + (x + 500) = 1500000

=> x + 1 +x + 2 + x + 3 + ... + x + 500 = 1500000

=> (x + x + ... + x) + (1 + 2 + 3 +... + 500) = 1500000

Số số hạng là : (500 - 1) : 1 + 1 = 500

Tổng : (1  + 500).500 : 2 = 125250

=> 500x + 125250 = 1500000

=> 500x = 1374750

=> x = 2749,5

( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ... + ( x + 500 ) = 1500000

x + x + x + ... + x ( 500 số x ) + 1 + 2 + 3 + ... + 500 = 1500000

Phần 1 + 2 + 3 + ... + 500 có  : ( 500 - 1 ) / 1 + 1 = 500 ( số hạng )

x * 500 + ( 500 + 1 ) * 500 / 2 = 1500000

x * 500 + 125250 = 1500000

x * 500 = 1500000 - 125250

x * 500 = 1374750

x = 1374750 / 500 = 2749,5

                                                     Bài giải

\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+500\right)=1500000\)

\(x+1+x+2+...+x+500=1500000\)

\(\left(x+x+...+x\right)\left(1+2+...+500\right)=1500000\)

\(500x+[\left(500-1\right)\text{ : }1+1]\text{ }\left(500+1\right)\text{ : }2=1500000\)

\(500x+125250=1500000\)

\(500x=1500000-125250\)

\(500x=1374750\)

\(x=1374750\text{ : }500\)

\(x=2749,5\)

( 500 x 9 - 250 x 2 x 9 ) x ( 1 + 2 + 3 .... +9 )

\(=9\times\left(500-250\times2\right)\times\left(1+2+...+9\right)\\ =9\times\left(500-500\right)\times\left(1+2+...+9\right)\\ =9\times0\times\left(1+2+...+9\right)=0\)

\(\left(500\cdot9-250\cdot2\cdot9\right)\cdot\left(1+2+3+...+9\right)\)

\(=\left(500\cdot9-500\cdot9\right)\left(1+2+3+...+9\right)\)

\(=0\cdot\left(1+2+3+...+9\right)=0\)

\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{x.\left(x+1\right)}=\dfrac{499}{500}\)

\(\Leftrightarrow1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{499}{500}\)

\(\Leftrightarrow1-\dfrac{1}{x+1}=\dfrac{499}{500}\)

\(\Leftrightarrow x=499\)

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