Question

1tính tổng

E=2+8+18+32+....+200

2tìm x biết 1.2+2.3+3.4+....+x.(x+1)=5850

Answer 1

2 ) 1.2 + 2.3 + 3.4 + ... + x.( x + 1 ) = 5850

Đặt A = 1.2 + 2.3 + 3.4 + ... + x.( x + 1 )

=> 3A = 1.2.3 + 2.3.( 4 - 1 ) + 3.4.(5 - 2 ) + ... + x.( x + 1 ). [ ( x + 2 ) - ( x - 1 ) ] 

= 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + x . ( x + 1 ) . ( x + 2 ) - ( x - 1 ). x . ( x + 1 )

= x . ( x + 1 ) . ( x + 2 )

=> A = [ x . ( x + 1 ) . ( x + 2 ) ] : 3

Mà tổng A = 5850

=> [ x . ( x + 1 ) . ( x + 2 ) ] : 3 = 5850

=> x . ( x + 1 ) . ( x + 2 ) = 17550

x . ( x + 1 ) . ( x + 2 ) = 25 . 26 . 27 

=> x = 25

Vậy x = 25