Question

tính nhanh :

                     1.2+2.3+3.4+......+1999.2000

Answer 1

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Answer 2

DE OT

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Answer 3

Gọi S = 1.2 + 2.3 + 3.4 + ....... + 1999.2000

<=> 3S = 1.2.3 + 2.3.3 + 3.4.3 + ...... + 1999.2000.3

<=> 3S = 1.2.3 + 2.3.( 4 - 1 ) + 3.4.( 5 - 2 ) + ..... + 1999.2000.( 2001 - 1998 )

<=> 3S = 1.2.3 + 2.3.4 -1.2.3 + 3.4.5 - 2.3.4 + ..... + 1999.2000.2001 - 1998.1999.2000

<=> 3S = 1999.2000.2001

=> S = ( 1999.2000.2001 ) : 3 

Answer 4

Đặt A =1.2+2.3+3.4+......+1999.2000

Ta có : A =1.2+2.3+3.4+......+1999.2000

=> 3A = 1 .2 . 3 + 2 . 3 . 3 + ......+ 1999 . 2000 . 3

=> 3A = 1. 2 . (3 - 0) + 2 . 3 . ( 4 - 1) + .... + 1999 . 2000 . (2001 - 1998 )

=> 3 A = 1 . 2 .3 - 0 . 1 . 2 + 2 . 3 .4 - 1 . 2 .3 + .........+ 1999 . 2000 . 2001 - 1998 . 2000 . 2001 

=> 3A = 1999 . 2000 . 2001 - 0 . 1  . 2

=> A = 1999 . 2000 . 2001  : 3 

=> A = 2666666000

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