1x2 + 2x3 + 3x4 + 4x5 + .... +99x100
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Tính tổng:
A = 1x2+3x4+4x5+...+99x100
B = 1x22+2x32+3x42+4x52+...+99x1002
M=1x2+2x3+3x4+4x5+....+99x100
3M = 1.2.3 + 2.3.(4-1) +..+ 99.100.(101-98)
3M = 1.2.3 + 2.3.4 - 1.2.3 + .... + 99.100.101 - 98.99.100
3M = 99.100.101 = 999900
M = 333300
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Gọi biểu thức trên là M, ta có :
M = 1x2 + 2x3 + 3x4 + 4x5 + ...+ 99x100
M x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3
A x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)
M x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100.
M x 3 = 99x100x101
M= 99x100x101 : 3
M = 333300
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A=1x2+2x3+3x4+4x5+...+99x100
A = 1 x 2 + 2 x 3 + 3 x 4 + ... + 99 x 100
3A = 1 x 2 x (3 - 0) + 2 x 3 x (4 - 1) + 3 x 4 x (5 - 2) + ... + 99 x 100 x (101 - 98)
3A = 1 x 2 x 3 - 0 x 1 x 2 + 2 x 3 x 4 - 1 x 2 x 3 + 3 x 4 x 5 - 2 x 3 x 4 + ... + 99 x 100 x 101 - 98 x 99 x 100
3A = (1 x 2 x 3 + 2 x 3 x 4 + 3 x 4 x 5 + ... + 99 x 100 x 101) - (0 x 1 x 2 + 1 x 2 x 3 + 2 x 3 x 4 + ... + 98 x 99 x 100)
3A = 99 x 100 x 101
A = 33 x 100 x 101
A = 333300
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A = 1x2+2x3+3x4+4x5+....+99x100
3A=1x2x(3-0)+2x3x(4-1)+3x4x(5-2)+...+99x100x(101-98)
3A= 1x2x3-0x1x2+2x3x4-1x2x3+3x4x5-2x3x4+...+99x100x101-98x99x100
3A= 99x100x101
A=999900 : 3 = 333300
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Tính nhanh:. A = 1x2 + 2x3 + 3x4 + 4x5 + ... + 99x100.
A = 1x2 + 2x3 + 3x4 + 4x5 + ...+ 99x100
A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3 A x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98) ..................................
A x 3 = 99x100x101 A = 333300
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Tính nhanh:.
A = 1x2 + 2x3 + 3x4 + 4x5 + ... + 99x100.
A = 1x2 + 2x3 + 3x4 + 4x5 + ...+ 99x100
A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3
A x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)
..................................
A x 3 = 99x100x101
A = 333300
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tính tổng:S= 1x2 + 2x3 + 3x4 + 4x5 +...+ 99x100
S= 1x2+2x3+3x4+4x5+...+98x99+99x100
Gọi biểu thức trên là A, ta có :
A = 1x2 + 2x3 + 3x4 + 4x5 + ...+ 99x100
A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3
A x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)
A x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100.
A x 3 = 99x100x101
A = 99x100x101 : 3
A = 333300
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tinh nhanh A = 1x2 + 2x3 + 3x4 + 4x5 +.............+ 99x100
A = 1x2 + 2x3 + ... + 99x100
3A = 1x2x3 + 2x3x(4-1) + ... + 99x100x(101-98)
3A = 1x2x3 + 2x3x4 - 1x2x3 + ... + 99x100x101 - 98x99x100
3A = 99x100x101
3A = 999900
A = 333300
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Ta có:
A=1x2+2x3+3x4+4x5+...+99x100
3A=1x2x3+2x3x3+3x4x3+4x5x3+...+99x100x3
3A=1x2x3+2x3x(4-1)+3x4x(5-2)+4x5x(6-3)+...+99x100x(101-98)
3A=1x2x3+2x3x4-1x2x3+3x4x5-2x3x4+4x5x6-3x4x5+...+99x100x101-98x99x100
Suy ra 3A=99x100x101
A=99x100x101/3
A=333300
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A = 1 . 2 + 2 . 3 + 3 . 4 + 4 . 5 +.............+ 99 . 100
A = 1 . 2 + 2 .3 + 3 . 4 + 4 . 5 + ...+ 99 . 100
A . 3 = 1 . 2 . 3 + 2 . 3 . 3 + 3 . 4 . 3 + 4. 5 . 3 + ... + 99 . 100 . 3
A . 3 = 1. 2 . 3 + 2 . 3 . (4-1) + 3 .4 . (5 - 2 ) + 4. 5 . (6- 3 )+... + 99 . 100. (101 -98 )
A . 3 = 1 . 2 . 3 + 2 . 3 . 4 - 1. 2 . 3 + 3 . 4 . 5 - 2 . 3 . 4 + 4 .5 . 6 - 3 . 4 . 5 + ... + 99 . 100 . 101 - 98 . 99.100.
A . 3 = 99 . 100 . 101
A = 99 . 100 . 101 : 3
A = 333 300
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Tính S= 1x2+2x3+3x4+4x5+...+99x100
A = 1x2 + 2x3 + 3x4 + 4x5 + ...+ 99x100
A x 3 = 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3
A x 3 = 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98)
A x 3 = 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100.
A x 3 = 99x100x101
A = 99x100x101 : 3
A = 333300
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