Xin hay nhất nhé tus ^_^
`a)` $2^{n}$ `-` $2^{n-3}$ `=` `112`
$2^{n}$ `-` $2^{n}$ . $2^{-3}$ `=` `112`
$2^{n}$`(1-` $2^{-3}$`)` `=` `112`
$2^{n}$`(1-`$\frac{1}{8}$`)` `=` `112`
$2^{n}$ . $\frac{7}{8}$ `=` `112`
$2^{n}$ `=` `112:`$\frac{7}{8}$
$2^{n}$ `=` `128`
$2^{n}$ `=` $2^{7}$
`→` `n=7` `∈ N`
Vậy `n=7`
`b)` `1+2+` $2^{2}$ `+...+` $2^{n+1}$ `=` `1023`
Đặt `A` `=` `1+2+` $2^{2}$ `+...+` $2^{n+1}$
`→` `2A` `=` `2+` $2^{2}$ `+` $2^{3}$ `+...+` $2^{n+2}$
`2A-A` `=` `(2+` $2^{2}$ `+` $2^{3}$ `+...+` $2^{n+2}$`)` `-` `(1+2+` $2^{2}$ `+...+` $2^{n+1}$`)`
`A` `=` $2^{n+2}$ `-` `1`
`→` $2^{n+2}$ `-` `1` `=` `1023`
$2^{n+2}$ `=` `1024`
$2^{n+2}$ `=` $2^{10}$
`→` `n+2=10`
`n =10-2`
`n =8` `∈N`
Vậy `n=8`
