Question

[Nijino Yume]

A=4+2^2+2^3+2^4+...+2^20

Dấu này ^ là mũ nha bạn 

làm đúng mình tick cho 3 cái

Answer 1

[❖︵Ňɠυүễη Çɦâυ Ƭυấη Ƙїệт♔]

\(A=4+2^2+2^3+2^4+...+2^{20}\)

\(\Rightarrow A=2^2+2^2+2^3+2^4+...+2^{20}\)

\(\Rightarrow 2A=2^3+2^3+2^4+2^5+...+2^{21}\)

\(\Rightarrow2A-A=2^{21}+2^3-2^2-2^2\)

\(\Rightarrow A=2^2\left(2^{19}+2-1-1\right)\)

\(\Rightarrow A=2^{19}.2^2=2^{21}\)

Answer 2

[Huỳnh Quang Sang]

\(\text{A}=4+2^2+2^3+2^4+...+2^{20}\)

\(\Rightarrow\text{A}=4+(2^2+2^3+...+2^{20})\)

\(\Rightarrow\text{A}-4=2^2+2^3+...+2^{20}\)

\(\Rightarrow2\text{(A}-4)=2^3+2^4+...+2^{21}\)

\(\text{A}-4=2(\text{A}-4)-(\text{A}-4)=(2^3+2^4+...+2^{21})-(2^2+2^3+...+2^{20})\)

\(\Rightarrow\text{A}-4=(2^3-2^3)+(2^4-2^4)+....+(2^{21}-2^2)\)

\(\Rightarrow\text{A}-4=2^{21}-4\)

\(\Rightarrow\text{A}=2^{21}-4+4\Rightarrow\text{A}=2^{21}\)

Chúc bạn hok tốt :>