Question

Tính tổng S = 3x4 + 4x5 + .......... + 49x50

Answer 1

3S = 3 X4 X 3 + 4 X 5 X 3 +................+ 49 X 50 X 3

3S = 3 X 4 X ( 5 - 2 ) + 4 X 5 X ( 6 - 3 ) + .................. + 49 X 50 X ( 51 - 48 )

3S = 3 X 4 X 5 - 2 X 3 X 4 + 4 X 5 X 6 - 3 X 4 X 5 +............ + 49 X 50 X 51 - 48 X 49 X 50

3S = - ( 2 X 3 X 4 ) + ( 3 X 4 X 5 - 3 X 4 X 5 ) + ( 4 X 5 X 6 - 4 X 5 X 6 ) + ........... + ( 48 X 49 X 50 - 48 X 49 X 50 ) + 49 X 50 X 51

3S = - ( 2 X 3 X 4 )     +           0                    +                0                 + ...........+                     0                      + 49 X 50 X 51

3S = - 24 +  124950

3S = 124926=> S = 124926 : 3  => S = 41642

Answer 2

Ta có : S = 3.4 + 4.5 + 5.6 +.....+49.50

=>3S = - 2.3.4 + 3.4.5 - 3.4.5 + ..... + 49.50.51

=> 3S = -24 + 49.50.51

=> 3S = -24 + 124950 = 124926

=> S = 124926/3 = 41642