A = 1 + 5 + 52 + 53 + ....+ 52017
A . 5 = 5 + 52 + 53 + 54 + .... + 52018
A . 5 - A = ( 5 + 52 + 53 + 54 + .... + 52018 ) - ( 1 + 5 + 52 + 53 + ......+ 52017 )
A . 4 = 52018 - 1
Ta có : 52018 - 1 + 1 = 5n + 1
52018 = 5n+1
Suy ra : 2018 = n + 1
2018 - 1 = n
2017 = n
chuẩn mình cũng làm thế
đó là đề thi khảo sát giữa học kì 1
Ta có:
\(A=1+5+5^2+5^3+...+5^{2017}\)
\(5A=5.\left(1+5+5^2+5^3+...+5^{2017}\right)\)
\(5A=5+5^2+5^3+5^4+...+5^{2018}\)
\(5A-A=\left(5+5^2+5^3+5^4+...+5^{2018}\right)-\left(1+5+5^2+5^3+...+5^{2017}\right)\)
\(4A=5^{2018}-1\)
\(\Rightarrow4A+1=5^{2018}-1+1\)
\(\Rightarrow4A+1=5^{2018}\)
\(\Rightarrow4A+1=5^{n+1}\)
\(\Rightarrow5^{2018}=5^{n+1}\)
\(\Rightarrow n+1=2018\)
\(\Rightarrow n=2017\)
