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A=100/1 x 2 + 100/2 x 3 + 100/3 x 4 +...+100/99 x 100
A/100=1/1 x 2 + 1/2 x 3 + 1/3 x 4 +...+1/99 x 100
A/100=2-1/1x2 + 3-2/2x3 + ... + 100-99/99x100
A/100=1-1/2 + 1/2-1/3+...+1/99-1/100
A/100=1-1/100
A/100=99/100
A=99/100x100=99
Vậy A=99.
Ta có:
\(\frac{100}{1.2}+\frac{100}{2.3}+\frac{100}{3.4}+...+\frac{100}{99.100}\)
\(\Rightarrow100.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)\)
\(\Rightarrow100.\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\right)\)
\(\Rightarrow100.\left(\frac{1}{1}-\frac{1}{100}\right)\Leftrightarrow100.\frac{99}{100}=99\)
A. \(\left(x+1\right)+\left(x+2\right)+......+\left(x+100\right)=5750\)
\(x+1+x+2+....+x+100=5750\)
\(100x+\left(1+2+3+.......+100\right)=5750\)
\(100x+5050=5750\)
\(100x=700\)
\(x=700:100=7\)
B. x+(1+2+......+100) = 2000
x + 5050 = 2000
x = 2000 - 5050
x= -3050
C. ( x-1 )+(x-2)+......+( x - 100 ) = 50
x-1+x-2+.........+x-100 = 50
100x + ( -1-2-........-100 ) = 50
100x + ( - 5050 ) = 50
100x = 50 + 5050
100 x = 5100
x = 5100 : 100
x = 51
A . \(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+100\right)=5750\)
\(\left(x+x+x+...+x\right)+\left(1+2+3+...+100\right)=5750\)
\(100x+5050=5750\)
\(100x=5750-5050\)
\(100x=700\)
\(\Rightarrow x=\frac{700}{100}=7\)
B. \(x+\left(1+2+3+4+5+....+100\right)=2000\)
\(x+\frac{\left(100+1\right).100}{2}=2000\)
\(x+5050=2000\)
\(\Rightarrow x=2000-5050=-3050\)
C. \(\left(x-1\right)+\left(x-2\right)+\left(x-3\right)+....+\left(x-100\right)=50\)
\(\left(x+x+x+...+x\right)-\left(1+2+3+...+100\right)=50\)
\(100x-5050=50\)
\(100x=5100\)
\(\Rightarrow x=\frac{5100}{100}=51\)
a. 16 569 330
24 425 739
b. 14 711 334
24 935 708
c. 23 222 460
28 495 512
d. 12 585 992
13 837 260
a.4674 x 3545
4563 x 5353
b.4521 x 3254 = 14711334
.4387 x 5684 = 24958869
c.4436 x 5235 = 23222460
5242 x 5436 = 28495512
d.3646 x 3452 = 12585992
3252 x 4255 = 13837260
Học tốt
\(x+\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+....+\left(x+100\right)=5353\)
\(x+\left(x+x+x+...+x\right)+\left(1+2+3+...+100\right)=5353\)
\(101x+\frac{\left(1+100\right)\times100}{2}=5353\)
\(101x+5050=5353\)
\(101x=5353-5050\)
\(101x=303\)
\(\Rightarrow x=3\)
x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ......... + ( x + 100 ) = 535
101 x + ( 1 + 2 + ... + 100 ) = 535
101x + 5050 = 535
101x = -4515
\(\Rightarrow x=-\frac{4545}{101}\)