Question

1 nhân 3  + 3 nhân 5 + 5 nhân 7 + ......... + 97 nhân 99
 

Answer 1

Đặt A = 1 x 3 + 3 x 5 + 5 x 7 + ....+ 97 x 99

=> 6A = 1 x 3 x 6 + 3 x 5 x 6 + 5 x 7 x6 + ...+ 97 x 99 x 6

6A = 1 x 3 x ( 5+1) + 3 x 5 x (7-1) + 5 x 7 x ( 9-3) + ...+ 97 x 99 x (101- 95)

6A = 1 x 3 x 5 + 1 x 3 + 3 x 5 x 7 - 1x3x5 + 5 x 7 x 9 - 3x5x7 + ...+ 97x99x101 - 95x97x99

6A = ( 1 x 3 + 1 x 3 x 5 + 3 x 5 x 7 + 5x7x9+...+97x99x101) - (1x3x5+3x5x7+...+95x97x99)

6A = 1 x 3 + 97x99x101

\(A=\frac{1x3+97x99x101}{6}=161651\)