Question

Bài 1: Tính 

a) S=1+3+3 mũ 2 +3 mũ 3 +...+3 mũ 100

b) A=1+3 mũ 2 +3 mũ 4 +...+3 mũ 100

Answer 1

\(a,S=1+3+3^2+....+3^{100}.\)

\(\Rightarrow3S=3+3^2+...+3^{101}\)

\(\Rightarrow3S-S=\left(3+3^2+...+3^{101}\right)-\left(1+3+....+3^{100}\right)\)

\(\Rightarrow2S=3^{101}-1\)

\(\Rightarrow S=\frac{3^{101}-1}{2}\)

\(b,A=1+3^2+3^4+...+3^{100}\)

\(\Rightarrow3^2A=3^2+3^4+...+3^{102}\)

\(\Rightarrow9A-A=\left(3^2+3^4+...+3^{102}\right)-\left(1+3^2+....+3^{100}\right)\)

\(\Rightarrow8A=3^{102}-1\)

\(\Rightarrow A=\frac{3^{102}-1}{8}\)

Answer 2

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