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![](https://rs.olm.vn/images/avt/0.png?1311)
3A =1.2.3 +2.3.(4-1) +3.4.(5-2) +4.5.(6-3)....+199.200.(201 -198)
= 1.2.3+2.3.4 -1.2.3 +3.4.5- 2.3.4 + 4.5.6 - 3.4.5 +......+ 199.200.201 -198.199.200
3A =199.200.201
A=199.200.67 =254600
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: A=1.2+2.3+...+198.199+199.200
=>3A=1.2.3+2.3.3+...+198.199.3
+199.200.3
=>3A=1.2.3+2.3(4-1)+...+
198.199(200-197)+199.200(201-198)
=>3A=1.2.3+2.3.4-1.2.3+...+198.199.200
-197.198.199+199.200.201-198.199.200
=>3A=199.200.201
=>A=199.200.67
A=39800.67
A=2666600
![](https://rs.olm.vn/images/avt/0.png?1311)
=2(1/2.3+1/3.4+...+1/199.200)
=2(1/2-1/3+1/3-1/4+...+1/99-1/100)
=2(1/2-1/100)
=2 . 49/100
=49/50
![](https://rs.olm.vn/images/avt/0.png?1311)
A=1.2+2.3+...+199.200
3A = 1.2.3 + 2.3.3 +...+ 199.200.3
3A = 1.2.(3 - 0) + 2.3.(4 - 1) +...+ 199.200. (201 - 198)
3A = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 +...+ 199.200.201 - 198.199.200
3A = (1.2.3 + 2.3.4 +...+ 199.200.201) - (0.1.2 + 1.2.3 +...+ 198.199.200)
3A = 199.200.201 - 0.1.2
3A = 199.200.201
A = \(\frac{199.200.201}{3}=2666600\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có :
A = 1.2 + 2.3 + 3.4 + ... + 198.199 + 199.200
= 1.(1 + 1) + 2.(2 + 1) + 3.(3 + 1) + ... + 198(198 + 1) + 199(199 + 1)
= (1^2 + 1) + (2^2 + 2) + (3^2 + 3) + ... + (198^2 + 198) + (199^2 + 199)
= (1 + 2 + 3 + 4....+ 198 + 199) + (1^2 + 2^2 + 3^2 + ...+ 198^2 + 199^2)
* Dễ chứng minh :
....1 + 2 + 3 +...+ n = n(n + 1)/2
.... 1^2 + 2^2 +...+ n^2 = [n(n + 1)(2n + 1)]/6
Suy ra : A = [199.(199 + 1)]/2 + [199.(199 + 1)(2.199 + 1)]/6 = 2666600
![](https://rs.olm.vn/images/avt/0.png?1311)
Đặt A = 1.2 + 2.3 + 3.4 + .... + 199.200
⇒ 3A = 1.2.3 + 2.3.3 + 3.4.3 + .... + 199.200.3
⇒ 3A = 1.2.3 + 2.3.( 4 - 1 ) + 3.4.( 5 - 2 ) + .... + 199.200.( 201 - 198 )
⇒ 3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 199.200.201 - 198.199.200
⇒ 3A = ( 1.2.3 - 1.2.3 ) + ( 2.3.4 - 2.3.4 ) + .... + ( 198.199.200 - 198.199.200 ) + 199.200.201
⇒ 3A = 199.200.201
⇒ 3A = \(\frac{199.200.201}{3}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
S = -5/1.2 + -5/2.3 + -5/3.4 + ... + -5/199.200
S= -5/1 - (-5)/2 +(-5)/2 - (-5)/3+....+ (-5)/199 - (-5)/200
S= -5/1 - (-5)/200
S= -5/1 + 5/200
S= -199/40
\(S=\frac{-5}{1\cdot2}+\frac{-5}{2\cdot3}+\frac{-5}{3\cdot4}+...+\frac{-5}{199\cdot200}\)
\(S=\frac{-5}{1}-\frac{-5}{2}+\frac{-5}{2}-\frac{-5}{3}+...+\frac{-5}{199}-\frac{-5}{200}\)
\(S=-5+\frac{5}{200}\)
\(S=-\frac{199}{40}\)
Bạn check lại nha, không chắc đâu =.=
![](https://rs.olm.vn/images/avt/0.png?1311)
`S = 1.2 + 2.3 + 3.4 + 4.5 + ... + 99.100.`
`3S = 1.2.3 + 2.3.(4-1) + 3.4.(5-4) + 4.5.(6-3) + ... + 99.100.(101-98)`
`3S = 1.2.3 + 2.3.4-1.2.3 + 3.4.5-4.5.6 + 4.5.6-3.4.5 + ... + 99.100.101-98.99.100`
`3S = 99.100.101`
`S = 33.100.101`
`S = 333300`
3S=1.2(3-0)+2.3(4-1)+.....+99.100(101-98)
=1.2.3-0.1.2+2.3.4-1.2.3+4.5.6-2.3.4+....+99.100.101-98-99-100
=99.100.101
S=33.100.101
=333300
Ta có: A=1.2+2.3+...+198.199+199.200
=>3A=1.2.3+2.3.3+...+198.199.3
+199.200.3
=>3A=1.2.3+2.3(4-1)+...+
198.199(200-197)+199.200(201-198)
=>3A=1.2.3+2.3.4-1.2.3+...+198.199.200
-197.198.199+199.200.201-198.199.200
=>3A=199.200.201
=>A=199.200.67
A=39800.67
A=2666600