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Đặt A = 1 + 2 + 3 + ... + 97 +98 + 99
A = 99 + 98 + 97 + ... + 3 + 2 + 1
2A = ( 99 + 1 ) + ( 98 + 2 ) + ( 97 + 3 ) + ... + ( 3 + 97 ) + ( 98 + 2 ) + ( 99 + 1 ) ( 99 cặp số )
2A = 100 + 100 + 100 + ... + 100 + 100 + 100 ( 99 số )
2A = 100 . 99
2A = 9900
A = 4950
Vậy A = 4950
Ta có :
1+2+3+....+99
= \(\frac{\left(1+99\right).99}{2}\)
\(=50.99\)
\(=4950\)
a) A = (200 - 1) . 201 = 200 . 201 - 201
B = (201-1) . 200 = 201.200 - 200
201 > 200 => 200.201 - 201 < 201.200 - 200
=> A < B
b) C = ( 34 + 1).53 - 18 = 34.53 + 53 - 18 = 34.53 + 35 = D
=> C = D
a ) ta có :
\(A=199.201=199\left(200+1\right)=199.200+199\)
\(B=200.200=200.\left(199+1\right)=199.200+200\)
Vì \(199.200+200>199.200+199\) nên \(B>A\)
b ) Ta có :
\(C=35.53-18=53.34+53-18=53.34+35=D\)
Vậy \(C=D\)
a) \(A=\left(3,1-2,5\right)-\left(-2,5+3,1\right)\)
\(A=0,6-0,6\)
\(A=0\)
b) \(B=\left(5,3-2,8\right)-\left(4+5,3\right)\)
\(B=2,5-7,3\)
\(B=-6,8\)
c) \(C=-\left(25-3+2,81\right)+3,251-\left(1-2,8\right)\)
\(C=-24,81+3,251+1,8\)
\(C=-19,759\)
`@` `\text {Ans}`
`\downarrow`
`a,`
`A =(3,1 - 2,5) - (-2,5 + 3,1)`
`= 3,1 - 2,5 + 2,5 - 3,1`
`= (3,1 - 3,1) + (-2,5+2,5)`
`= 0`
Vậy, `A = 0`
`b,`
`B = (5,3 - 2,8) - (4+5,3)`
`= 5,3 - 2,8 - 4 - 5,3`
`= (5,3 - 5,3) + (-2,8-4)`
`= -6,8`
Vậy, `B = -6,8`
`c,`
`C = -(25 - 3 + 2,81) + 3,251 - (1 - 2,8)` `?`
`= -25 + 3 - 2,81 + 3,251 - 1 + 2,8`
`= (-25 + 3 - 1) + (-2,81 + 2,8) + 3,251`
`= -23 - 0,01 + 3,251`
`= -19,759`
C1: vì 198chia hết cho 9 mà 423 cung chia het cho 9 nên A chia hết cho 9
c2 có 594chia hết cho 9 mà 620 ko chia hết cho 9
còn lai thì.........vao gưi tin nhan nhe
ahihi
\(A=-5,13:\left(5\dfrac{5}{28}-1\dfrac{8}{9}.1,25+1\dfrac{16}{63}\right)\)
\(=-5,13:\left(\dfrac{145}{28}-\dfrac{17}{9}.\dfrac{125}{100}+\dfrac{79}{63}\right)\)
\(=-5,13:\left(\dfrac{145}{28}-\dfrac{17}{9}.\dfrac{5}{4}+\dfrac{79}{63}\right)\)
\(=-5,13:\left(\dfrac{145}{28}-\dfrac{85}{36}+\dfrac{79}{63}\right)\)
\(=-5,13:\dfrac{57}{14}=-5,13:\dfrac{15}{57}\)
\(=\dfrac{-71,82}{57}=1,26\)
Vậy \(A=1,26\)
\(B=\left(3\dfrac{1}{3}.1,9+19,5:4\dfrac{1}{3}\right).\left(\dfrac{62}{75}-\dfrac{4}{25}\right)\)
\(=\left(\dfrac{10}{3}.1,9+19,5:\dfrac{13}{3}\right).\left(\dfrac{62-12}{75}\right)\)
\(=\left(\dfrac{19}{3}+\dfrac{58,5}{13}\right).\dfrac{50}{75}\)
\(=\left(\dfrac{19}{3}+4,5\right).\dfrac{2}{3}\)
\(=\dfrac{32,5}{3}.\dfrac{2}{3}=\dfrac{65}{9}=7\dfrac{2}{9}\)
Vậy \(B=7\dfrac{2}{9}\)
\(\frac{ab}{a+b}=\frac{bc}{b+c}=\frac{ac}{a+c}\Leftrightarrow\frac{a+b}{ab}=\frac{b+c}{bc}=\frac{a+c}{ac}\Leftrightarrow\frac{1}{b}+\frac{1}{a}=\frac{1}{b}+\frac{1}{c}=\frac{1}{c}+\frac{1}{a}\)
\(\Leftrightarrow\frac{1}{a}=\frac{1}{b}=\frac{1}{c}\Leftrightarrow a=b=c\)
\(\Rightarrow\left(a-b\right)^3+\left(b-c\right)^3+\left(c-a\right)^3=\left(a-a\right)^3+\left(b-b\right)^3+\left(c-c\right)^3=0\)
b) B = 22 + 42 + 62 + ... + 982
\(\frac{1}{4}B=1^2+2^2+3^2+...+49^2\)
\(\frac{1}{4}B=1+2\left(1+1\right)+3\left(2+1\right)+...+49\left(48+1\right)\)
\(\frac{1}{4}B=1+2+1.2+2.3+3+...+48.49+49\)
\(\frac{1}{4}B=\left(1+2+3+...+49\right)+\left(1.2+2.3+...+48.49\right)\)
đặt A = 1.2 + 2.3 +...+ 48.49 ta có:
A = 1.2 + 2.3 +...+ 48.49
3A = 1.2.3 + 2.3.( 4 - 1) + ... + 48.49.( 50 - 47 )
3A = 1.2.3 + 2.3.4 - 1.2.3 +...+ 48.49.50 - 47.48.49
3A = 48.49.50
A = \(\frac{48.49.50}{3}=39200\)
thay A = 39200 vào \(\frac{1}{4}B\) ta có:
\(\frac{1}{4}B=\left(1+2+3+...+49\right)+39200\)
\(\frac{1}{4}B=1225+39200\)
\(\frac{1}{4}B=40425\)
B = 40425.4
B = 161700
vậy B = 161700
3A=1.2.3+2.3.4+3.4.3+.......+99.100.3
3A=1.2.(3-0) + 2.3 (4-1) + 3.4 . (5-2)+.......+ 99.100(101-98)
3A=(1.2.3+2.3.4+3.4.5+......+98.99.100)-(0.1.2+1.2.3+.....+98.99.100)
3A=99.100.101-0
3A=999900
A=999900:3
A=333300
a) |-137| + |-363|=137 + 363 = 500;
b) |-28| - |98| = 28 – 98 = -(98 – 28) = - 70;
c) (-200) - |-25|.|3| = (-200) – 25 . 3 = (-200) – 75 = -(200 + 75) = -275
a: =137+363=500
b: =28-98=-70
c: =-200-75=-275