A=6+18+36+60+...+29700+30300
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A = 6 + 18 + 36 + 60 + ... + 29700 + 30300
A = 3x1x2 + 3x2x3 + 3x3x4 + 3x4x5 + ... + 3x99x100 + 3x100x101
A = 3 x ( 1x2 + 2x3 + 3x4 + ... + 99x100 + 100x101)
A x 3 = 3 x 3 x ( 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3 + 100x101x3 )
A x 3 = 3 x 3 x ( 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98) + 100x101x(102-99)
A x 3 = 3 x 3 x ( 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100 + 100x101x102 - 99x100x101)
A x 3 = 3 x 3 x ( 100x101x102) A x 3 = 9 x 1030200
A x 3 = 9271800 A = 9271800 : 3
A = 3090600
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(x+1)3=27
(x+1)3=3 3
=>x+1=3
x=3-1
x=2
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A=6+18+36+60+...+29700+30300
A=3.(2+6+12+20+...+9900+10100)
Đặt B=2+6+12+20+...+9900+10100
B=1.2+2.3+3.4+4.5+...+99.100+100.101
3B=1.2.3+2.3.3+3.4.3+4.5.3+...+99.100.3+100.101.3
3B=1.2.3+2.3.(4-1)+3.4.(5-2)+4.5.(6-3)+...+99.100.(101-98)+100.101.(102-99)
3B=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+100.101.102-99.100.101
3B=100.101.102
B=100.101.102:3=343400
A=3.B=3.343400=1030200
Giải
Số số hạng là:
(30300-6):12+1=2525,5
Tổng A là:
(30300+6)x2525,5:2=38268901,6
Vậy tổng A là 38268901,5
A = 6 + 18 + 36 + 60 + ... + 29700 + 30300
A = 3x1x2 + 3x2x3 + 3x3x4 + 3x4x5 + ... + 3x99x100 + 3x100x101
A = 3 x ( 1x2 + 2x3 + 3x4 + ... + 99x100 + 100x101)
A x 3 = 3 x 3 x ( 1x2x3 + 2x3x3 + 3x4x3 + 4x5x3 + ... + 99x100x3 + 100x101x3 )
A x 3 = 3 x 3 x ( 1x2x3 + 2x3x(4-1) + 3x4x(5-2) + 4x5x(6-3) + ... + 99x100x(101-98) + 100x101x(102-99)
A x 3 = 3 x 3 x ( 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 + 4x5x6 - 3x4x5 + ... + 99x100x101 - 98x99x100 + 100x101x102 - 99x100x101)
A x 3 = 3 x 3 x ( 100x101x102)
A x 3 = 9 x 1030200
A x 3 = 9271800
A = 9271800 : 3
A = 3090600
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