Question

Answer 1

30

 

Answer 2

a) \(S=3^0+3^2+3^4+...+3^{2002}\)

\(\Rightarrow3^2S=3^2+3^4+...+3^{2004}\)

\(\Rightarrow8S=3^2+3^4+...+3^{2004}-3^0-3^2-...-3^{2002}=3^{2004}-1\)

\(\Rightarrow S=\dfrac{3^{2004}-1}{8}\)

b) \(S=3^0+3^2+3^4+...+3^{2002}\)

\(=\left(1+3^2+3^4\right)+3^6\left(1+3^2+3^4\right)+...+3^{1998}\left(1+3^2+3^4\right)\)

\(=91+3^6.91+...+3^{1998}.91\)

\(=91\left(1+3^6+...+3^{1998}\right)=7.13.\left(1+3^6+...+3^{1998}\right)⋮7\)