Question

Tính kết quả 

\(M=1+5+5^2+5^3+...+5^{2015}+5^{2016}\)

Answer 1

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Answer 2

\(M=1+5+5^2+5^3+...+5^{2015}+5^{2016}\)

=> \(5M=5+5^2+5^3+5^4+...+5^{2016}+5^{2017}\)

\(5M-M=\left(5+5^2+5^3+5^4+...+5^{2016}+5^{2017}\right)-\left(1+5+5^2+5^3+...+5^{2015}+5^{2016}\right)\)

\(\Rightarrow4M=5+5^2+5^3+...+5^{2017}-1-5-5^2-5^3-...-5^{2016}\)

\(4M=5^{2017}-1\)

\(\Rightarrow M=\frac{5^{2017}-1}{4}\)