`a) S=5+5^2+5^3+5^4+...+5^66`
`S=(5+5^2+5^3)+(5^4+5^5+5^6)+...+(5^64+5^65+5^66)`
`S=5(1+5+5^2)+5^4(1+5+5^2)+...+5^64(1+5+5^2)`
`S=5.31+5^4 .31+...+5^64 .31`
`S=31(5+5^4+...+5^64)`
`b) S=5+5^2+5^3+5^4+...+5^66`
`=> 5S=5^2+5^3+5^4+5^5+...+5^67`
`=> 5S-S=(5^2+5^3+5^4+5^5+...+5^67)-(5+5^2+5^3+5^4+...+5^66)`
`=> 4S=5^67-5`
- Ta có :
`16.5^(x+3)+21.5^x=2021.(4S+5)`
`16.5^x .5^3+21.5^x=2021.(5^67-5+5)`
`(16.5^3).5^x+21.5^x=2021.5^67`
`(16.125).5^x+21.5^x=2021.5^67`
`2000.5^x+21.5^x=2021.5^67`
`(2000+21).5^x=2021.5^67`
`2021.5^x=2021.5^67`
`=> 5^x=5^67`
`=> x=67`
