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![](https://rs.olm.vn/images/avt/0.png?1311)
A = 1 x 2 + 2 x 3 + 3 x 4 + ... + 99 x 100
3 x A = 1 x 2 x 3 + 2 x 3 x ( 4 - 1 ) + ... + 99 x 100 x ( 101 - 98 )
3 x A = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + ... + 99 x 100 x 101 - 98 x 99 x 100
3 x A = 99 x 100 x 101 = 999900
A = 999900 : 3 = 333300
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A = 1 – 2 + 3 – 4 + 5 – 6 +……… + 99 – 100 + 101
A = ( 1 + 3 + 5 + 7 …+ 101) – ( 2 + 4 + 6 + ….. + 100)
*Từ 1 đến 101 có: (101 – 1) : 2 + 1 = 51 số hạng nên:
1 + 3 + 5 + 7 +... +101 = (1 + 101) x 51 : 2 = 2601
*Từ 2 đến 100 có : (100 – 2) : 2 + 1 = 50 số hạng nên:
2 + 4 + 6 + 8 +.... + 100 = ( 2 + 100) x 50 : 2 = 2550
Ta có : A = 2601 – 2550
Vậy : A = 51
Đáp số: A = 51
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a
so so hang
(100-1):1+1=100(so hang)
tong bang
(100+1)x100:2=5050
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Đặt A=1*2+2*3+3*4+...........+99*100
3A=1*2*3+2*3*(4-1)+3*4*(5-2)+............+99*100*(101-98)
3A=1*2*3+2*3*4-1*2*3+3*4*5-2*3*4+................+99*100*101-98*99*100
3A=99*100*101
A=99*100*101:3
A=333300
![](https://rs.olm.vn/images/avt/0.png?1311)
số số hạng là :
(100 - 1) + 1=100 (số)
Tổng là :
( 100 + 1 )x 100 : 2 = 5050
![](https://rs.olm.vn/images/avt/0.png?1311)
tổng trên bằng:
1-3+2-4+...+97-99+98-100=-2+-2+...+-2+-2
=(-2)x50=-100
tính nhanh (2/3+3/4+5/6+...+99/100).(1/2+2/3+3/4+...+98/99)-(1/2+1/3+...+99/100).(2/3+2/4+...+98/99)
![](https://rs.olm.vn/images/avt/0.png?1311)
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2S=1x2x3+2x3x3+3x4x3+...+98x99x3+99x100x3
3S=1x2x3+2x3x(4-1)+3x4x(5-2)+...+98x99x(100-97)+99x100x(101-98)
3S=1x2x3-1x2x3+2x3x4-2x3x4+3x4x5-...-97x98x99+98x99x100-98x99x100+99x100x101=99x100x101
S=33x100x101=333300
3xS = 1x 2x 3 + 2x3x3 + 3x4x3 + ...+ 98x99x3 + 99x100x3
= 1x2x3 + 2x3x(4-1) + 3x4x(5-2) +...+98x99x(100-97) + 99x100x(101-98)
= 1x2x3 -1x2x3 + 2x4x4 -2x3x4 + 3x4x5 +...- 97x98x99 +98x99x100 -98x99x199 + 99x100x101
= 99x100x101 = 999900
=> S = 999900 : 3 =333300
![](https://rs.olm.vn/images/avt/0.png?1311)
A = 1 x 2 + 2 x 3 + 3 x 4 + ... + 99 x 100
3A = 1 x 2 x 3 + 2 x 3 x ( 4 - 1 ) + 3 x 4 x ( 5 - 2 ) + .... + 99 x 100 x ( 101 - 98 )
3A = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + ... + 99 x 100 x 101 - 98 x 99 x 100
3A = 99 x 100 x 101
3A = 999900
A = 999900 : 3
A = 333300
S = 1 x 2 + 2 x 3 + ... + 99 x 100
3S = 1 x 2 x 3 + 2 x 3 x (4 - 1) + ..... + 99 x 100 x (101 - 98)
3S = 1 x 2 x 3 + 2 x 3 x 4 - 1 x 2 x 3 + .... + 99 x 100 x 101 - 98 x 99 x 100
3S = 99 x 100 x 101 = 999900
S = 999900 : 3 = 333300