Question

[Lê Minh Đức]

Tìm A

4+4²+4³+.....+4³⁰

Answer 1

[༺༒༻²ᵏ⁸]

\(A=4+4^2+4^3+...+4^{30}\)

\(4A=4^2+4^3+4^4+...+4^{31}\)

\(4A-A=\left(4^2+4^3+4^4+...+4^{31}\right)-\left(4+4^2+4^3+...+4^{30}\right)\)

\(3A=4^2+4^3+4^4+...+4^{31}-4-4^2-4^3-...-4^{30}\)

\(3A=4^{31}-4\)

\(A=\dfrac{4^{31}-4}{3}\)

Answer 2

[Trương Nhật Minh]

\(A=4+4^2+4^3+...+4^{30}\\ \Rightarrow4A=4^2+4^3+...+4^{31}\\ \Rightarrow4A-A=4^{31}-4\\ \Rightarrow A=\dfrac{4^{31}-4}{3}\)