Duong Ha

2 tuần trước

tính 2/4.7+2/7.10+2/10.13+...+2/73.76

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Apple347

2 tuần trước

Answer

Đặt: $2/{4 . 7} + 2/{7 . 10} + 2/{10 . 13} + ... + 2/{73 . 76} = A$

$A = 2/{4 . 7} + 2/{7 . 10} + 2/{10 . 13} + ... + 2/{73 . 76}$

$A = 3/3 . (2/{4 . 7} + 2/{7 . 10} + 2/{10 . 13} + ... + 2/{73 . 76})$

$A = 2/3 . (3/{4 . 7} + 3/{7 . 10} + 3/{10 . 13} + ... + 3/{73 . 76})$

$A = 2/3 . (1/4 - 1/7 + 1/7 - 1/10 + 1/10 - 1/13 + ... + 1/73 - 1/76)$

$A = 2/3 . (1/4 - 1/76)$

$A = 2/3 . 9/38$

$A = 3/19$

Vậy $A = 3/19$

Osakaff

2 tuần trước

$A = 2/(4.7) + 2/(7.10) + ... + 2/(73.76)$

$A = 2/3 . ( 3/(4.7) + 3/(7.10) + ... + 3/(73.76) )$

$A = 2/3 . ( 1/4 - 1/7 + 1/7 - 1/10 + ... + 1/(73) - 1/(76) )$

$A= 2/3 . ( 1/4 - 1/(76) )$

$A = 2/3 . 9/(38)$

$A= 3/(19)$

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