S = 1 x 3 + 2 x 4 + 3 x 5 + 4 x6 + ...+ 49 x 51 + 50 x 52
S = ( 1 x3 + 3 x5 + ..+ 49x51) + (2x4+4x6+...+50x52)
Đặt A = 1x3+3x5+...+49x51
=> 6A = 1x3x6+3x5x6+...+49x51x6
6A = 1x3x(5+1) + 3x5x(7-1) + ...+ 49x51x(53-47)
6A = 1x3x5 + 1x3 + 3x5x7 - 1x3x5 + ...+ 49x51x53 - 47x49x51
6A = (1x3 + 1x3x5 + 3x5x7+...+49x51x53) - (1x3x5+...+47x49x51)
6A = 1x3 + 49x51x53
A = 22 075
Tương tự như trên ta có: B = 2x4 + 4x6 + ...+ 50x52
B = 23 400
Thay B ;A vào S
S = 22 075 +23 400
S = 45 475
S = 1 x 3 + 2 x 4 + 3 x 5 + 4 x6 + ...+ 49 x 51 + 50 x 52
S = ( 1 x3 + 3 x5 + ..+ 49x51) + (2x4+4x6+...+50x52)
Đặt A = 1x3+3x5+...+49x51
=> 6A = 1x3x6+3x5x6+...+49x51x6
6A = 1x3x(5+1) + 3x5x(7-1) + ...+ 49x51x(53-47)
6A = 1x3x5 + 1x3 + 3x5x7 - 1x3x5 + ...+ 49x51x53 - 47x49x51
6A = (1x3 + 1x3x5 + 3x5x7+...+49x51x53) - (1x3x5+...+47x49x51)
6A = 1x3 + 49x51x53
A = 22 075
Tương tự như trên ta có: B = 2x4 + 4x6 + ...+ 50x52
B = 23 400
Thay B ;A vào S
S = 22 075 +23 400
S = 45 475
S=1*(2+1)+2*(3+1)+3*(4+1)+4*(5+1)*............*49*(50+1)+50*(51+1)
=1*2+2*3+3*4+4*5+.................+49*50+50*51+(1+2+3+4+...................+49+50)
3S=1*2*(3-0)+2*3*(4-1)+3*4*(5-2)+..............+49*50*(52-49)+50*51*(53-50)
3S=1*2*3+2*3*4+3*4*5+...................+49*50*51+50*51*52-0*1*2-1*2*3-2*3*4-............48*49*50-49*50*51
3S=50*51*52=132600
S=44200