\(A=5+5^3+5^5+...+5^{99}\)
\(\Rightarrow25A=5^3+5^5+5^7+...+5^{101}\)
\(\Rightarrow25A-A=\left(5^3+5^5+5^7+...+5^{101}\right)-\left(5+...+5^{99}\right)\)
\(\Rightarrow24A=5^{101}-5\)
\(\Rightarrow A=\dfrac{5^{101}-5}{24}\)
Vậy \(A=\dfrac{5^{101}-5}{24}\)
\(5+5^3+5^5+...+5^{97}+5^{99}\)
\(\Rightarrow25A=5^2\left(5+5^3+5^5+...+5^{99}\right)\)
\(\Rightarrow25A=5^3+5^5+5^7+...+5^{101}\)
\(\Rightarrow25A-A=5^3+5^5+...+5^{99}+5^{101}-5-5^3-5^5-...-5^{99}\)
\(\Rightarrow24A=5^{101}-5\)
\(\Rightarrow A=\dfrac{5^{101}-5}{24}\)
Đặt A = 5 + 53 + 55 + ... + 597 + 599
=> 52A = 53 + 55 + ... + 599 + 5101
=> 25A - A = 5101 - 5
=> 24A = 5101 - 5
=> A = \(\dfrac{5^{101}-5}{24}\)
@Yuuki Tenpouin
