Question

thu gọn tổng g = 3^300 - 3mũ 99 + 3mũ98 - 3mũ97 +.... + 3^2 + 3 + 1

Answer 1

Sửa đề: \(G=3^{100}-3^{99}+3^{98}-3^{97}+\cdots+3^2-3+1\)

Ta có: \(G=3^{100}-3^{99}+3^{98}-3^{97}+\cdots+3^2-3+1\)

=>\(3G=3^{101}-3^{100}+3^{99}-3^{98}+\cdots+3^3-3^2+3\)

=>\(3G+G=3^{101}-3^{100}+3^{99}-3^{98}+\cdots+3^3-3^2+3+3^{100}-3^{99}+3^{98}-3^{97}+\cdots+3^2-3+1\)

=>\(4G=3^{101}+1\)

=>\(G=\frac{3^{101}+1}{4}\)