cho B=1/11+1/11^2+1/11^3+.....+1/11^100. so sánh B và 1/10

`B = 1/11 + 1/11^2 + 1/11^3 + ... + 1/ ( 11^{100} )`

`=> 11B = 11 . ( 1/11 + 1/11^2 + 1/11^3 + ... + 1/ ( 11^{100} ) )`

`=> 11B = 1 + 1/11 + 1/11^2 + ... + 1/ ( 11^{99 } )`

`=> 11B - B = ( 1 + 1/11 + 1/11^2 + ... + 1/ ( 11^{99} ) ) -`

`( 1/11 + 1/11^2 + 1/11^3 + ... + 1/ ( 11^{100} ) )`

 `=> 10B = 1 - 1/ ( 11^{100} )`

`=> B = 1/10 - 1/( 10 . 11^{100} )`

Mà `:` `1/ ( 10 . 11^{100} ) > 0`

`=> B < 1/10`

Vậy `: B < 1/10`