Question

Answer 1

\(A=1+5+5^2+...+5^{50}\)

\(5A=5+5^2+5^3+...+5^{51}\)

\(5A-A=\left(5+5^2+5^3+...+5^{51}\right)-\left(1+5+5^2+...+5^{50}\right)\)

\(4A=5^{51}-1\Rightarrow A=\dfrac{5^{51}-1}{4}\)

Answer 2

\(A=1+5+5^2+5^3+...+5^{50}\)

\(\Rightarrow5A=5+5^2+5^3+5^4+...+5^{51}\)

\(5A-A=4A=\left(5+5^2+5^3+5^4+...+5^{51}\right)-\left(1+5+5^2+5^3+...+5^{50}\right)\)\(\Rightarrow4A=5^{51}-1\)

\(\Rightarrow A=\dfrac{5^{51}-1}{4}\)