`a)` `S= 5 + 5^2 + 5^3 +...+ 5^2020`
`=>5S = 5^2 + 5^3 + 5^4 +...+ 5^2021`
`=>5S-S = ( 5^2 + 5^3 + 5^4 +...+ 5^2021 ) - ( 5 + 5^2 + 5^3 +...+ 5^2020 )`
`=>4S = 5^2021 - 5`
`=>S= ( 5^2021 - 5 )/4`
`b)` `S= 5 + 5^2 + 5^3 +...+ 5^2020`
`=>S=(5+5^3)+(5^2 + 5^4)+...+(5^2018 + 5^2020)`
`=>S=5.(1+5^2) + 5^2 . (1+5^2) +...+ 5^2018 . (1+5^2)`
`=>S=5^2 + (5+ 5^2 +...+ 5^2018) \vdots 26`
`=>S=26+ (5+ 5^2 +...+ 5^2018) \vdots 26`
`=>S \vdots 26`