Question

giá trị số tự nhiên n thõa mãn : 1+2+2^2+2^3+...+2^32=2^n-1

Answer 1

Rút gọn vế trái ta được 2^33-1

=> n = 33

Answer 2

Đặt \(A=1+2+2^2+2^3+......+2^{31}+2^{32}\)

Ta có:

\(A=1+2+2^2+2^3+......+2^{31}+2^{32}\)

\(\Leftrightarrow2A=2+2^2+2^3+......+2^{32}+2^{33}\)

\(\Leftrightarrow2A-A=\left(2+2^2+2^3+......+2^{32}+2^{33}\right)-\left(1+2+2^2+2^3+......+2^{31}+2^{32}\right)\)

\(\Leftrightarrow A=2^{33}-1\)

Mặt khác \(A=2^n-1\)

\(\Rightarrow2^{33}-1=2^n-1\)

\(\Rightarrow2^{33}-1-2^n+1=0\)

\(\Rightarrow2^{33}-2^n=0\)

\(\Rightarrow2^{33}=2^n\)

\(\Rightarrow n=33\)

Vậy n=33