Question

[Lê Thì Hà Thành]

2¹⁰⁰-2⁹⁹+2⁹⁸-2⁹⁷+...+2²

Answer 1

[Le Thi Khanh Huyen]

Đặt \(A=2^{100}-2^{99}+2^{98}-2^{97}+...-2^3+2^2\)

\(=\left(2^{100}-2^{99}\right)+\left(2^{98}-2^{97}\right)+...+\left(2^4-2^3\right)+4\)

\(=2^{99}\left(2-1\right)+2^{97}\left(2-1\right)+...+2^3\left(2-1\right)+4\)

\(=\left(2^3+2^5+...+2^{97}+2^{99}\right)+4\)

Đặt \(B=2^3+2^5+...+2^{97}+2^{99}\)

\(\Rightarrow4B=2^5+2^7+...+2^{99}+2^{101}\)

\(\Rightarrow4B-B=3B=2^{101}-2^3\)

\(B=\frac{2^{101}-2^3}{3}\)

\(A=B+4\)

\(=\frac{2^{101}-2^3}{3}+4\)

\(=\frac{2^{101}-8+12}{3}\)

\(=\frac{2^{101}+4}{3}\)

Answer 2

[Hollow Ichigo 3]

Bạn lấy đâu ra nhiều hình thế Nobita Kun