Question

Cho A=\(5\)+\(5^2\)+\(5^3\)+...+\(5^{2022}\) .Tìm x để 4A+5=\(5^x\)

Answer 1

\(A=5+5^2+5^3+...+5^{2022}\)

\(5A=5^2+5^3+5^4+...+5^{2023}\)

\(5A-A=5^{2023}-5\)

\(4A+5=5^{2023}-5+5\)

\(4A+5=5^{2023}\)

Vì \(4A+5=5^x\)

\(=>5^x=5^{2023}\)

\(=>x=2023\)

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