Question

6²+6⁴+6⁶+...+6⁹⁸+6¹⁰⁰

Answer 1

Đặt \(A=6^2+6^4+6^6+...+6^{98}+6^{100}\)

Ta có: \(A=6^2+6^4+6^6+...+6^{98}+6^{100}\)

\(\Leftrightarrow36A=6^4+6^6+...6^{100}+6^{102}\)

\(\Leftrightarrow A-36A=6^2+6^4+6^6+...6^{98}+6^{100}-6^4-6^6-...-6^{100}-6^{102}\)

\(\Leftrightarrow-35\cdot A=6^2-6^{102}\)

\(\Leftrightarrow A=\dfrac{6^{102}-6^2}{35}\)