Question

Tìm số tự nhiên n; biết 2^n-1-2-2^2-2^3-2^4-....-2^100=1

GIẢI LẬP LUẬN NHA CÁC BẠN HỌC!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

TA CO 2^n-1-2^2-....-2^100=1

=>2n-(1+2^2+2^3+...+2^100)=1

dat A=1+2^2+2^3+...+2^100

=>2A=2+2^3+2^4+...+2^101

=>2A-A=(2+2^2+2^3+...+2^101)-(1+2+2^2+...+2^100)

=>A=2+2^2+2^3+...+2^101-1-2-2^2-..-2^100

=>A=2^101-1

=>2^n-(2^101-1)=1

=>2^n-2^101+1=1

=>2^n=1-1+2^101

=>2^n=2^101=>n=101

Vay n=101.

Answer 2

 ^{2^n-1-2^2-....-2^100=1}

^{=>2n-(1+2^2+2^3+...+2^100)=1}

^{dat A=1+2^2+2^3+...+2^100}

^{=>2A=2+2^3+2^4+...+2^101}

^{=>2A-A=(2+2^2+2^3+...+2^101)-(1+2+2^2+...+2^100)}

^{=>A=2+2^2+2^3+...+2^101-1-2-2^2-..-2^100}

^{=>A=2^101-1}

^{=>2^n-(2^101-1)=1}

^{=>2^n-2^101+1=1}

^{=>2^n=1-1+2^101}

^{=>2^n=2^101}=>n=101

Vay n=101.