(2+4+6+...+100) - (1+3+5+...+99) = ?
1 x 2 + 2 x 3 + 3 x 4 + ... + 99 x 100 = ?
3 x 4 + 4 x 5 + 5 x 6 + ... + 149 x 150 = ?
1 + (1 + 2) + ( 1 + 2 + 3) + (1 + 2 + 3 + 4) + ....... + (1 + 2 + 3 + ... + 99)
----------------------------------------------------------------------------------------------------------- ( gạch ngang phân số )
1 x 99 + 2.98 + 3.97 + ...... + 99 x 1
Đặt S = 1*2 + 2*3 + 3*4 + ........+ 99*100
=> 3S = 1.2.3 + 2.3.3+3.4.3+...+99.100.3
=> 3S = 1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+...+99.100.(101-98)
=> 3S = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4+...+99.100.101 - 98.99.100
=> 3S = 99.100.101 = 999900
=>S = 333300
Đặt S = 1*2 + 2*3 + 3*4 + ........+ 99*100
=> 3S = 1.2.3 + 2.3.3+3.4.3+...+99.100.3
=> 3S = 1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+...+99.100.(101-98)
=> 3S = 1.2.3 - 0.1.2 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4+...+99.100.101 - 98.99.100
=> 3S = 99.100.101 = 999900
=>S = 333300
Đảm bảo đúng!!!