Question

Answer 1

\(B=5^2+5^3+5^4+...+5^{2018}\)

\(\Rightarrow5B=5^3+5^4+5^5+...+5^{2019}\)

\(\Rightarrow4B=5B-B=5^3+5^4+5^5+...+5^{2019}-5^2-5^3-5^4-...-5^{2018}=5^{2019}-5^2\)

\(\Rightarrow B=\dfrac{5^{2019}-5^2}{4}\)

\(C=4-4^2+4^3-4^4+...+4^{97}-4^{98}+4^{99}\)

\(\Rightarrow4C=4^2-4^3+4^4-...-4^{99}+4^{100}\)

\(\Rightarrow5C=4C+C=4^2-4^3+4^4-...-4^{99}+4^{100}+4-4^2+4^3-...-4^{98}+4^{99}=4^{100}+4\)

\(\Rightarrow C=\dfrac{4^{100}+4}{5}\)