(x+1)+(x+2)+(x+3)+...+(x+500)=1500000
TÌM X
(x+1)+(x+2)+(X+3)+...+(x+30)=500
\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+30\right)=500\)
Số lượng số hạng là: \(30-1+1=30\)
\(\Rightarrow30x+\dfrac{30\left(30+1\right)}{2}=500\)
\(30x+465=500\)
\(30x=35\)
\(x=\dfrac{7}{6}\)
\(\left(x+1\right)+\left(x+2\right)+...+\left(x+30\right)=500\)
\(\Rightarrow x+1+x+2+..+x+30=500\)
\(\Rightarrow\left(x+x+...+x\right)+\left(1+2+...+30\right)=500\)
\(\Rightarrow30\cdot x+465=500\)
\(\Rightarrow30\cdot x=500-465\)
\(\Rightarrow30\cdot x=35\)
\(\Rightarrow x=\dfrac{35}{30}\)
\(\Rightarrow x=\dfrac{7}{6}\)
( 500 x 9 - 250 x 2 x 9 ) x ( 1 + 2 + 3 .... +9 )
( 500 x 9 - 250 x 2 x 9 ) x ( 1 + 2 + 3 .... +9 )
\(=9\times\left(500-250\times2\right)\times\left(1+2+...+9\right)\\ =9\times\left(500-500\right)\times\left(1+2+...+9\right)\\ =9\times0\times\left(1+2+...+9\right)=0\)
\(\left(500\cdot9-250\cdot2\cdot9\right)\cdot\left(1+2+3+...+9\right)\)
\(=\left(500\cdot9-500\cdot9\right)\left(1+2+3+...+9\right)\)
\(=0\cdot\left(1+2+3+...+9\right)=0\)
b) 200 x 4 = ...... 300 x 2 = ......
200 x 2 = ...... 300 x 3 = ......
400 x 2 = ...... 500 x 1 = ......
100 x 4 = ...... 100 x 3 = ......
b) 200 x 4 = .800..... 300 x 2 = ..600....
200 x 2 = .400..... 300 x 3 = ...900...
400 x 2 = ...800... 500 x 1 = ..500....
100 x 4 = ..400.... 100 x 3 = .300.....
Tính nhanh: 500 x 4 x 2 x 25 - 500 x 3 x 2 x 30
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
1/1 x 10 + 1/2 x 15 + 1/3 x 20+...........................................+1/98 x 495 + 1/99 x 500
(500 x 9 - 250 x 18) x (1 + 2 + 3 + .... + 9)
1/1*2 + 1/2*3 +1/3*4 +.....+ 1/x(x+1) =499/500
Hãy tìm x
Tính nhẩm:
Cách làm: 200 x 3 = ?
Nhẩm: 2 trăm x 3 = 6 trăm
Vậy: 200 x 3 = 600
200 x 2 = 300 x 2 =
200 x 4 = 400 x 2 =
100 x 5 = 500 x 1 =
Học sinh nhẩm và ghi kết quả như sau:
200 x 2 = 400
200 x 4 = 800
100 x 5 = 500
300 x 2 =600
400 x 2 =800
500 x 1 =500
200 x 2 = 400 300 x 2 =600
200 x 4 = 800 400 x 2 =800
100 x 5 = 500 500 x 1 =500
Tìm X:
1/1 x 2 +1/2 x 3+ 1/3 x 4 + .........+1/ X x ( X +1) = 499/500
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ta có:
1-1/2+1/2-1/3+1/3-1/4+....+1/x -1/x+1 =499/500
1-1/x+1 =499/500
1/x+1 =1/500
x+1=500
x=499
\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{X\times\left(X+1\right)}=\frac{499}{500}\)
\(\Leftrightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{X}-\frac{1}{X+1}=\frac{499}{500}\)
\(\Leftrightarrow1-\frac{1}{X+1}=\frac{499}{500}\)
\(\Leftrightarrow\frac{1}{X+1}=\frac{1}{500}\)
\(\Leftrightarrow X+1=500\)
\(\Leftrightarrow X=499\)