`S = 1+5+5^2+...+5^2024`
`=> 5S = 5 + 5^2 + 5^3+..+5^2025`
`=> 5S-S = (5 + 5^2 + 5^3+..+5^2025) - (1+5+5^2+...+5^2024)`
`=> 4S = 5^2025 - 1`
`=> 4S + 1 = 5^2025 -1 + 1 = 5^2025`
`=> 4S +1 = 5^n`
`=> 5^2025 = 5^n`
`=> n = 2025`
Vậy `n = 2025`
\(1+5+5^2+...+5^{2024}\)
a,
Đặt \("1+5+5^2+...+5^{2024}"\) là `S`
Ta có :
\(S=1+5+5^2+...+5^{2024}\)
\(5S=5+5^2+5^3+...+5^{2025}\)
\(5S-S=\left(5+5^2+5^3+...+5^{2024}\right)-\left(1+5+5^2+...+5^{2024}\right)\)
\(4S=5^{2024}-1\)
\(S=\dfrac{5^{2024}-1}{4}\)
`b,`
\(4\times\dfrac{5^{2024}-1}{4}+1=5^n\)
\(\Rightarrow5^{2024}-1+1=5^n\)
\(\Rightarrow5^{2024}=5^n\)
\(\Rightarrow n=2024\)
