a) \(S=7^0+7^2+7^4+...+7^{2018}\)
\(\Rightarrow7^2S=7^2\left(7^0+7^2+7^4+...+7^{2018}\right)\)
\(49S=\left(7^2+7^4+7^6+...+7^{2020}\right)\)
\(49S-S=48S=\left(7^2+7^4+7^6+...+7^{2020}\right)-\left(7^0+7^2+7^4+...+7^{2018}\right)\)
\(48S=7^{2020}-7^0=7^{2020}-1\Leftrightarrow S=\dfrac{7^{2020}-1}{48}\) vậy \(S=\dfrac{7^{2020}-1}{48}\)
b) ta có : \(S=7^0+7^2+7^4+...+7^{2018}\)
\(S=\left(7^0+7^2\right)+\left(7^4+7^6\right)+...+\left(7^{2016}+7^{2018}\right)\)
\(S=\left(1+49\right)+7^4\left(1+7^2\right)+...+7^{2016}\left(1+7^2\right)\)
\(S=\left(50\right)+7^4\left(1+49\right)+...+7^{2016}\left(1+49\right)\)
\(S=50+7^4\left(50\right)+...+7^{2016}\left(50\right)\)
\(S=50\left(1+7^4+...+7^{2016}\right)⋮5\)
vậy \(S\) chia hết cho \(5\) (đpcm)
