M = 5 + 52 + ... + 5100
5M = 52 + 53 + ... + 5101
5M - M = (52 + 53 + ... + 5101) - (5 + 52 + ... + 5100)
4M = 5101 - 5
4M + 5 = 5101 = 5n
=> n = 101
Vậy n = 101
\(M=5+5^2+...+5^{100}\)
\(5M=5^2+5^3+...+5^{101}\)
\(5M-M=\left(5^2+5^3+...+5^{101}\right)-\left(5+5^2+...+5^{100}\right)\)
\(4M=5^{101}-5\)
\(4M+5=5^{101}-5+5\)
\(5^n=5^{101}\)
n = 101
Ta có:
\(M=5+5^2+...+5^{100}\)
\(\Rightarrow5M=5^2+5^3+...+5^{101}\)
\(\Rightarrow5M-M=\left(5^2+5^3+...+5^{101}\right)-\left(5+5^2+...+5^{100}\right)\)
\(\Rightarrow4M=5^{101}-5\)
Mà \(4M+5=5^n\)
\(\Rightarrow5^{101}-5+5=5^n\)
\(\Rightarrow5^{101}=5^n\)
\(\Rightarrow n=101\)
Vậy n = 101
