\(S = 5+5^2+5^3+5^4+...+\)\(5^{2017}\)
\(\Rightarrow5S=5^2+5^3+5^4+...+5^{2018}\)
\(\Rightarrow4S=5S-S=5^{2018}-5\)
\(\Rightarrow S=\dfrac{5^{2018}-5}{4}\)
S=\(5+5^2+...+5^{2017}\)
=>5S=5.(\(5+5^2+...+5^{2017}\))
=>5S=\(5^2+5^3+...+5^{2018}\)
=>5S-S=(\(5^2+5^3+...+5^{2018}\))-(\(5+5^2+...+5^{2017}\))
=>4S=\(5^{2018}-5\)
=>S=(\(5^{2018}-5\)):4
\(S=5+5^2+5^3+5^4+...+5^{2017}\)
\(5S=5^2+5^3+..+5^{2018}\)
\(5S-S=\left(5^2+5^3+..+5^{2018}\right)-\left(5+5^2..+5^{2017}\right)\)
\(4S=5^{2018}-5\)
\(S=\dfrac{5^{2018}-5}{4}\)
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