tính giá trị của biểu thức A =1/31[31/5(9-1/2)-17/2(4+1/5)]+1/2+1/6+1/12+...+1/930

Giải thích các bước giải:

`A = 1/31[31/5(9 - 1/2) - 17/2(4 + 1/5)] + 1/2 + 1/6 + ........... + 1/930`

`A = 1/31(31/5 . 17/2 - 17/2 . 21/5) + (1/(1 . 2) + 1/(2 . 3) + ......... + 1/(30 . 31))`

`A = 1/31 . [17/2 . (31/5 - 21/5)] + (1 - 1/2 + 1/2 - 1/3 + ............ + 1/30 - 1/31)`

`A = 1/31 . 17/2 . 2 + (1 - 1/31)`

`A = 17/31 + 30/31`

`A = 47/31`

`A = 1/31 [31/5 ( 9 - 1/2) - 17/2 (4 + 1/5)] + 1/2 + 1/6 + 1/12 + ... + 1/930`

`=> A = 1/31 [31/5 . 17/2 - 17/2 . 21/5] + (1/(1.2) + 1/(2.3) + 1/(3.4) + ... + 1/(30.31))`

`=> A = 1/31 [17/2 . (31/5 - 21/5)] + (1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/30 - 1/31 )`

`=> A = 1/31 [17/2 . 2] + (1/1 - 1/31)`

`=> A = 1/31 . 17 + 30/31`

`=> A = 17/31 + 30/31`

`=> A = 47/31`

Vậy `A = 47/31`

`#dtkc`