A = 5 + 52 + 53 + ... + 52017
5A = 52 + 53 + 54 + ... + 52018
5A - A = (52 + 53 + 54 + ... + 52018) - (5 + 52 + 53 + ... + 52017)
4A = 52018 - 5
4A + 5 =52018
4A + 5 = 5.52017
=> x = 52017
\(A=5+5^2+5^3+...+5^{2017}.\)
\(\Rightarrow5A=5^2+5^3+5^4+...+5^{2018}\)
\(\Rightarrow5A-A=4A=\left(5^2+5^3+...+5^{2018}\right)-\left(5+5^2+...+5^{2017}\right)\)
\(=5^{2018}-5\)
\(\Rightarrow4A+5=5X\)
\(\Leftrightarrow5^{2018}-5+5=5X\)
\(\Leftrightarrow5^{2018}=5X\)
\(\Rightarrow X=5^{2017}\)
A = 5 + 52 + 53 + ... + 52017
5A = 52 + 53 + 54 + ... + 52018
5A - A = (52 + 53 + 54 + ... + 52018) - (5 + 52 + 53 + ... + 52017)
4A = 52018 - 5
4A + 5 =52018
4A + 5 = 5.52017
=> x = 52017
