Question

[Hiền Nguyễn]

Cho A= 4 + 2 mũ 2 +2 mũ 3+ 2 mũ 4 +....+2 mũ 20

Tính A?

Answer 1

[Tẫn]

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

Đặt \(B=2^2+2^3+2^4+....+2^{20}\)

\(\Rightarrow2B=2^3+2^4+2^5+...+2^{21}\)

\(\Rightarrow2B-B=\left(2^3+2^4+2^5+...+2^{21}\right)-\left(2^2+2^3+2^4+...+2^{20}\right)\)

\(\Rightarrow B=2^{21}-2^2\)

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

\(\Rightarrow A=2^{21}\) 

Answer 2

[Nguyễn Linh Chi]

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

\(2.A=8+2^3+2^4+...+2^{21}\)

\(\Rightarrow2A-A=8+2^{21}-4-2^2=2^{21}\)

Suy ra A= 2 mũ 21