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
Ta có:
\(A=1.2+2.3+3.4+...+99.100\)
\(\Rightarrow3A=1.2.\left(3-0\right)+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+99.100.\left(101-98\right)\)
\(\Rightarrow3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100\)
\(\Leftrightarrow3A=99.100.101\Leftrightarrow A=\frac{99.100.101}{3}=333300\)
\(B=1.2.3+2.3.4+4.5.6+...+98.99.100\)
\(\Rightarrow4B=1.2.3.\left(4-0\right)+2.3.4.\left(5-1\right)+4.5.6.\left(7-3\right)+...+98.99.100.\left(101-97\right)\)
\(\Rightarrow4B=1.2.3.4+2.3.4.5-1.2.3.4+4.5.6.7-3.4.5.6+...+98.99.100.101-97.98.99.100\)
\(\Leftrightarrow4B=98.99.100.101\Leftrightarrow B=\frac{98.99.100.101}{4}=24497550\)
A= 1 x 2 + 2 x 3 + 3 x 4 +........+ 99 x 100
=> 2 + 6 + 12 +........+ 9900
=> 8 + 12 +.....+ 9900
=> 20 +....+ 9900
=> 20 + 20 + 30 +....+ 9900
=> 70 +....+ 9900
=> ( 9900 x 70 ) : 2
=> 693000 : 2
=> 346500
B = 1 x 2 x 3 + 2 x 3 x 4 +......+ 98 x 99 x100
=> ( 1 x 2 x 3) + ( 2 x 3 x 4 ) +....+ ( 98 x 99 x 100 )
= 6 + 24 +.......+ 970200
=> 28 + 120 +...+ 970200
=> ( 148 x 970200 ) : 2
=> 143589600 : 2
=> 71794900
A = 1.2 + 2.3 + .... + 99.100
3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ..... + 99.100.101
3A = 99.100.101
A = 99.100.101/3 = 333300
Ta có:
\(A=1\times2+2\times3+...+99\times100\)
\(3A=1\times2\times\left(3-0\right)+2\times3\times\left(4-1\right)+...+99\times100\times\left(101-98\right)\)
\(3A=1\times2\times3+2\times3\times4-1\times2\times3+...+99\times100\)
\(3A=99\times100\times101\)
\(A=\frac{99\times100\times101}{3}=333300\)
Vậy \(A=333300\)
Ta có:
\(B=1\times2\times3+2\times3\times4+...+98\times99\times100\)
\(4B=1\times2\times3\times\left(4-0\right)+2\times3\times4\times\left(5-1\right)+...+98\times99\times100\)
\(4B=1\times2\times3\times4+2\times3\times4\times5-1\times2\times3\times4+...+98\times99\times100\times101\)\(-97\times98\times99\times100\)
\(4B=98\times99\times100\times101\)
\(B=\frac{98\times99\times100\times101}{4}=24497550\)
Vậy \(B=24497550\)
