a, \(A=3^0+3^1+3^2+...+3^{100}\)
\(\Rightarrow3A=3+3^2+3^3+...+3^{101}\)
\(\Rightarrow3A-A=\left(3+3^2+3^3+...+3^{101}\right)-\left(1+3+3^2+...+3^{100}\right)\)
\(\Rightarrow2A-3^{101}-1\)
\(\Rightarrow A=\frac{3^{101}-1}{2}\)
Vậy : \(A=\frac{3^{101}-1}{2}\)
b, \(C=5^0+5^1+5^2+...+5^{18}\)
\(\Rightarrow5C=5^1+5^2+5^3+...+5^{19}\)
\(\Rightarrow5C-C=\left(5^1+5^2+5^3+...+5^{19}\right)-\left(5^0+5^1+5^2+...+5^{18}\right)\)
\(\Rightarrow4C=5^{19}-1\)
\(\Rightarrow C=\frac{5^{19}-1}{4}\)
Vậy : \(C=\frac{5^{19}-1}{4}\)
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