Question

A=\(3^{100}-3^{99}+3^{98}-3^{97}+...+3^2-3+1\)

\(\frac{15^3+5.15^2-5^3}{18^3+6.18^2-6^3}\)

Answer 1

Gọi giá trị trên là : A

\(A=3^{100}-3^{99}+3^{98}+....+3^2-3+1\)

\(\Rightarrow3A=3^{101}-3^{100}+3^{99}-3^{98}+......+3^3-3^2+3\)

\(\Rightarrow3A+A=3^{101}+1\)

\(\Rightarrow4A=3^{101}+1\Rightarrow A=\frac{3^{101}+1}{4}\)

Answer 2

3³×5³+5×3²×5²-5³/ 6³+3³+ 6×6²×3²-6³=5³×(3³+3²- 1)/6³×(3³+3²-1)=5³/6³⁼125/216