Question

Tính các tổng sau 

  2/11x13 + 2/13 x15 + 2/15 x17 + ............ + 2/95x97 +2/97x9 = ?

  1 x 2 + 2 x 3 + 3 x 4 + 4 x 5 .......... + 99 x 100 = ?

Answer 1

Đặt A =  1.2 + 2.3 + 3.4 +.......... + 99.100

=> 3A = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ..... + 99.100.(101 - 98)

=> 3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ....... + 99.100.101 - 98.99.100

=> 3A = (1.2.3 + 2.3.4 + 3.4.5 + ....... + 99.100.101) - (1.2.3 + 2.3.4 + ......... + 98.99.100)

=> 3A = 99.100.101

=> A = 99.100.101 : 3 = 999900

Answer 2

2/11x13+2/13x15+2/15x17+....+2/95x97+2/97x99

=1/11-1/13+1/13-1/15+1/15-1/17+....+1/95-1/97+1/97-1/99

=1/11-1/99

=9/99-1/99

=8/99

đúng nhé bạn

Answer 3

Đặt A =  1.2 + 2.3 + 3.4 +.......... + 99.100

=> 3A = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ..... + 99.100.(101 - 98)

=> 3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ....... + 99.100.101 - 98.99.100

=> 3A = (1.2.3 + 2.3.4 + 3.4.5 + ....... + 99.100.101) - (1.2.3 + 2.3.4 + ......... + 98.99.100)

=> 3A = 99.100.101

=> A = 99.100.101 : 3 = 999900