Ta có:
\(A=1-5+5^2-5^3+-.+5^{98}-5^{99}\)
\(\Rightarrow5A=5-5^2+5^3-5^4+-..+5^{99}-5^{100}\)
\(\Rightarrow5A+A=\left(5-5^2+5^3-5^4+-...+5^{99}-5^{100}\right)+\left(1-5+5^2-5^3+-..+5^{98}-5^{99}\right)\)
\(\Rightarrow6A=-5^{100}+1\)
\(\Rightarrow A=\dfrac{1-5^{100}}{6}\)
Chúc bạn học tốt!!!
